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vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Propriétés_de_l'addition"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Propriétés de l'addition</span> </div> </a> <ul id="toc-Propriétés_de_l'addition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Propriétés_de_la_multiplication" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Propriétés_de_la_multiplication"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Propriétés de la multiplication</span> </div> </a> <ul id="toc-Propriétés_de_la_multiplication-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Factorisation_et_développement" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Factorisation_et_développement"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Factorisation et développement</span> </div> </a> <ul id="toc-Factorisation_et_développement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliographie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliographie"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bibliographie</span> </div> </a> <button aria-controls="toc-Bibliographie-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Bibliographie</span> </button> <ul id="toc-Bibliographie-sublist" class="vector-toc-list"> <li id="toc-Ouvrages" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ouvrages"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Ouvrages</span> </div> </a> <ul id="toc-Ouvrages-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Articles_d'encyclopédies" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Articles_d'encyclopédies"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Articles d'encyclopédies</span> </div> </a> <ul id="toc-Articles_d'encyclopédies-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sommaire" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Basculer la table des matières" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Basculer la table des matières</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Algèbre classique</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Aller à un article dans une autre langue. Disponible en 56 langues." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-56" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">56 langues</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Elementare_Algebra" title="Elementare Algebra – alémanique" lang="gsw" hreflang="gsw" data-title="Elementare Algebra" data-language-autonym="Alemannisch" data-language-local-name="alémanique" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1_%D8%A7%D8%A8%D8%AA%D8%AF%D8%A7%D8%A6%D9%8A" title="جبر ابتدائي – arabe" lang="ar" hreflang="ar" data-title="جبر ابتدائي" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%81lxebra_elemental" title="Álxebra elemental – asturien" lang="ast" hreflang="ast" data-title="Álxebra elemental" data-language-autonym="Asturianu" data-language-local-name="asturien" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Элементар алгебра – bachkir" lang="ba" hreflang="ba" data-title="Элементар алгебра" data-language-autonym="Башҡортса" data-language-local-name="bachkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Элементарная алгебра – biélorusse" lang="be" hreflang="be" data-title="Элементарная алгебра" data-language-autonym="Беларуская" data-language-local-name="biélorusse" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BC%D1%8D%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D1%8C%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Элемэнтарная альгебра – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Элемэнтарная альгебра" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Елементарна алгебра – bulgare" lang="bg" hreflang="bg" data-title="Елементарна алгебра" data-language-autonym="Български" data-language-local-name="bulgare" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%BE%E0%A6%A5%E0%A6%AE%E0%A6%BF%E0%A6%95_%E0%A6%AC%E0%A7%80%E0%A6%9C%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="প্রাথমিক বীজগণিত – bengali" lang="bn" hreflang="bn" data-title="প্রাথমিক বীজগণিত" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Elementarna_algebra" title="Elementarna algebra – bosniaque" lang="bs" hreflang="bs" data-title="Elementarna algebra" data-language-autonym="Bosanski" data-language-local-name="bosniaque" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80lgebra_elemental" title="Àlgebra elemental – catalan" lang="ca" hreflang="ca" data-title="Àlgebra elemental" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AC%DB%95%D8%A8%D8%B1%DB%8C_%D8%B3%DB%95%D8%B1%DB%95%D8%AA%D8%A7%DB%8C%DB%8C" title="جەبری سەرەتایی – sorani" lang="ckb" hreflang="ckb" data-title="جەبری سەرەتایی" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Element%C3%A1rn%C3%AD_algebra" title="Elementární algebra – tchèque" lang="cs" hreflang="cs" data-title="Elementární algebra" data-language-autonym="Čeština" data-language-local-name="tchèque" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BB%C4%83_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Элементарлă алгебра – tchouvache" lang="cv" hreflang="cv" data-title="Элементарлă алгебра" data-language-autonym="Чӑвашла" data-language-local-name="tchouvache" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Elementare_Algebra" title="Elementare Algebra – allemand" lang="de" hreflang="de" data-title="Elementare Algebra" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%84%CE%BF%CE%B9%CF%87%CE%B5%CE%B9%CF%8E%CE%B4%CE%B7%CF%82_%CE%AC%CE%BB%CE%B3%CE%B5%CE%B2%CF%81%CE%B1" title="Στοιχειώδης άλγεβρα – grec" lang="el" hreflang="el" data-title="Στοιχειώδης άλγεβρα" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Elementary_algebra" title="Elementary algebra – anglais" lang="en" hreflang="en" data-title="Elementary algebra" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Baza_algebro" title="Baza algebro – espéranto" lang="eo" hreflang="eo" data-title="Baza algebro" data-language-autonym="Esperanto" data-language-local-name="espéranto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81lgebra_elemental" title="Álgebra elemental – espagnol" lang="es" hreflang="es" data-title="Álgebra elemental" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Oinarrizko_aljebra" title="Oinarrizko aljebra – basque" lang="eu" hreflang="eu" data-title="Oinarrizko aljebra" data-language-autonym="Euskara" data-language-local-name="basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1_%D9%85%D9%82%D8%AF%D9%85%D8%A7%D8%AA%DB%8C" title="جبر مقدماتی – persan" lang="fa" hreflang="fa" data-title="جبر مقدماتی" data-language-autonym="فارسی" data-language-local-name="persan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81lxebra_elemental" title="Álxebra elemental – galicien" lang="gl" hreflang="gl" data-title="Álxebra elemental" data-language-autonym="Galego" data-language-local-name="galicien" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%91%D7%A1%D7%99%D7%A1%D7%99%D7%AA" title="אלגברה בסיסית – hébreu" lang="he" hreflang="he" data-title="אלגברה בסיסית" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%B0%E0%A4%AE%E0%A5%8D%E0%A4%AD%E0%A4%BF%E0%A4%95_%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="प्रारम्भिक बीजगणित – hindi" lang="hi" hreflang="hi" data-title="प्रारम्भिक बीजगणित" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Elemi_algebra" title="Elemi algebra – hongrois" lang="hu" hreflang="hu" data-title="Elemi algebra" data-language-autonym="Magyar" data-language-local-name="hongrois" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%A1%D6%80%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B0%D5%A1%D5%B6%D6%80%D5%A1%D5%B0%D5%A1%D5%B7%D5%AB%D5%BE" title="Տարրական հանրահաշիվ – arménien" lang="hy" hreflang="hy" data-title="Տարրական հանրահաշիվ" data-language-autonym="Հայերեն" data-language-local-name="arménien" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Algebra_elementari" title="Algebra elementari – interlingua" lang="ia" hreflang="ia" data-title="Algebra elementari" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Aljabar_elementer" title="Aljabar elementer – indonésien" lang="id" hreflang="id" data-title="Aljabar elementer" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Algebra_elementare" title="Algebra elementare – italien" lang="it" hreflang="it" data-title="Algebra elementare" data-language-autonym="Italiano" data-language-local-name="italien" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%88%9D%E7%AD%89%E4%BB%A3%E6%95%B0%E5%AD%A6" title="初等代数学 – japonais" lang="ja" hreflang="ja" data-title="初等代数学" data-language-autonym="日本語" data-language-local-name="japonais" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B4%88%EB%93%B1%EB%8C%80%EC%88%98%ED%95%99" title="초등대수학 – coréen" lang="ko" hreflang="ko" data-title="초등대수학" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Algebra_elementaris" title="Algebra elementaris – latin" lang="la" hreflang="la" data-title="Algebra elementaris" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Aljebra_fundal" title="Aljebra fundal – lingua franca nova" lang="lfn" hreflang="lfn" data-title="Aljebra fundal" data-language-autonym="Lingua Franca Nova" data-language-local-name="lingua franca nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%9E%E0%BA%B6%E0%BA%94%E0%BA%8A%E0%BA%B0%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94%E0%BA%9E%E0%BA%B7%E0%BB%89%E0%BA%99%E0%BA%96%E0%BA%B2%E0%BA%99" title="ພຶດຊະຄະນິດພື້ນຖານ – lao" lang="lo" hreflang="lo" data-title="ພຶດຊະຄະນິດພື້ນຖານ" data-language-autonym="ລາວ" data-language-local-name="lao" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Aljabar_elementer" title="Aljabar elementer – minangkabau" lang="min" hreflang="min" data-title="Aljabar elementer" data-language-autonym="Minangkabau" data-language-local-name="minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Елементарна алгебра – macédonien" lang="mk" hreflang="mk" data-title="Елементарна алгебра" data-language-autonym="Македонски" data-language-local-name="macédonien" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Algebra_permulaan" title="Algebra permulaan – malais" lang="ms" hreflang="ms" data-title="Algebra permulaan" data-language-autonym="Bahasa Melayu" data-language-local-name="malais" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Elementaire_algebra" title="Elementaire algebra – néerlandais" lang="nl" hreflang="nl" data-title="Elementaire algebra" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Element%C3%A6r_algebra" title="Elementær algebra – norvégien bokmål" lang="nb" hreflang="nb" data-title="Elementær algebra" data-language-autonym="Norsk bokmål" data-language-local-name="norvégien bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Alg%C3%A8bra_element%C3%A0ria" title="Algèbra elementària – occitan" lang="oc" hreflang="oc" data-title="Algèbra elementària" data-language-autonym="Occitan" data-language-local-name="occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D8%A8%D8%AA%D8%AF%D8%A7%D8%A6%DB%8C_%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="ابتدائی الجبرا – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ابتدائی الجبرا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81lgebra_elementar" title="Álgebra elementar – portugais" lang="pt" hreflang="pt" data-title="Álgebra elementar" data-language-autonym="Português" data-language-local-name="portugais" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Элементарная алгебра – russe" lang="ru" hreflang="ru" data-title="Элементарная алгебра" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B8%E0%B7%96%E0%B6%BD%E0%B7%92%E0%B6%9A_%E0%B7%80%E0%B7%93%E0%B6%A2_%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA" title="මූලික වීජ ගණිතය – cingalais" lang="si" hreflang="si" data-title="මූලික වීජ ගණිතය" data-language-autonym="සිංහල" data-language-local-name="cingalais" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Elementary_algebra" title="Elementary algebra – Simple English" lang="en-simple" hreflang="en-simple" data-title="Elementary algebra" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Елементарна алгебра – serbe" lang="sr" hreflang="sr" data-title="Елементарна алгебра" data-language-autonym="Српски / srpski" data-language-local-name="serbe" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Element%C3%A4r_algebra" title="Elementär algebra – suédois" lang="sv" hreflang="sv" data-title="Elementär algebra" data-language-autonym="Svenska" data-language-local-name="suédois" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%9F%E0%AE%BF%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%9F%E0%AF%88_%E0%AE%87%E0%AE%AF%E0%AE%B1%E0%AF%8D%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="அடிப்படை இயற்கணிதம் – tamoul" lang="ta" hreflang="ta" data-title="அடிப்படை இயற்கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="tamoul" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Alhebrang_elementaryo" title="Alhebrang elementaryo – tagalog" lang="tl" hreflang="tl" data-title="Alhebrang elementaryo" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Temel_cebir" title="Temel cebir – turc" lang="tr" hreflang="tr" data-title="Temel cebir" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Елементарна алгебра – ukrainien" lang="uk" hreflang="uk" data-title="Елементарна алгебра" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%A8%D8%AA%D8%AF%D8%A7%D8%A6%DB%8C_%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="ابتدائی الجبرا – ourdou" lang="ur" hreflang="ur" data-title="ابتدائی الجبرا" data-language-autonym="اردو" data-language-local-name="ourdou" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_s%C6%A1_c%E1%BA%A5p" title="Đại số sơ cấp – vietnamien" lang="vi" hreflang="vi" data-title="Đại số sơ cấp" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamien" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%88%9D%E7%AD%89%E4%BB%A3%E6%95%B0" title="初等代数 – wu" lang="wuu" hreflang="wuu" data-title="初等代数" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A2%D7%9C%D7%A2%D7%9E%D7%A2%D7%A0%D7%98%D7%90%D7%A8%D7%A2_%D7%90%D7%9C%D7%92%D7%A2%D7%91%D7%A8%D7%A2" title="עלעמענטארע אלגעברע – yiddish" lang="yi" hreflang="yi" data-title="עלעמענטארע אלגעברע" data-language-autonym="ייִדיש" data-language-local-name="yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%88%9D%E7%AD%89%E4%BB%A3%E6%95%B8" title="初等代數 – chinois" lang="zh" hreflang="zh" data-title="初等代數" data-language-autonym="中文" data-language-local-name="chinois" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%9F%BA%E6%9C%AC%E4%BB%A3%E6%95%B8" title="基本代數 – cantonais" lang="yue" hreflang="yue" data-title="基本代數" data-language-autonym="粵語" data-language-local-name="cantonais" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q211294#sitelinks-wikipedia" title="Modifier les liens interlangues" class="wbc-editpage">Modifier les liens</a></span></div> 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mw-parser-output" lang="fr" dir="ltr"><div class="bandeau-container metadata bandeau-article bandeau-niveau-ebauche"><div class="bandeau-cell bandeau-icone" style="display:table-cell;padding-right:0.5em"><span class="noviewer" typeof="mw:File"><a href="/wiki/Fichier:Evariste_galois.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Evariste_galois.jpg/27px-Evariste_galois.jpg" decoding="async" width="27" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Evariste_galois.jpg/41px-Evariste_galois.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Evariste_galois.jpg/54px-Evariste_galois.jpg 2x" data-file-width="792" data-file-height="1024" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p><strong class="bandeau-titre">Cet article est une <a href="/wiki/Aide:%C3%89bauche" title="Aide:Ébauche">ébauche</a> concernant l’<a href="/wiki/Alg%C3%A8bre" title="Algèbre">algèbre</a>.</strong> </p><p>Vous pouvez partager vos connaissances en l’améliorant (<b><a href="/wiki/Aide:Comment_modifier_une_page" title="Aide:Comment modifier une page">comment ?</a></b>) selon les recommandations des <a href="/wiki/Projet:Accueil" title="Projet:Accueil">projets correspondants</a>. </p> </div></div> <div class="bandeau-container metadata homonymie hatnote"><div class="bandeau-cell bandeau-icone" style="display:table-cell;padding-right:0.5em"><span class="noviewer" typeof="mw:File"><a href="/wiki/Aide:Homonymie" title="Aide:Homonymie"><img alt="Page d’aide sur l’homonymie" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/20px-Logo_disambig.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/30px-Logo_disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/40px-Logo_disambig.svg.png 2x" data-file-width="512" data-file-height="375" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p>Pour les articles homonymes, voir <a href="/wiki/Alg%C3%A8bre_(homonymie)" class="mw-disambig" title="Algèbre (homonymie)">Algèbre (homonymie)</a>. </p> </div></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Algebraproblem.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Algebraproblem.jpg/220px-Algebraproblem.jpg" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Algebraproblem.jpg/330px-Algebraproblem.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Algebraproblem.jpg/440px-Algebraproblem.jpg 2x" data-file-width="818" data-file-height="512" /></a><figcaption>Exemple de calculs d'algèbre élémentaire.</figcaption></figure> <p>L'<b>algèbre élémentaire</b>, également appelée <b>algèbre classique</b> est la branche des <a href="/wiki/Math%C3%A9matiques" title="Mathématiques">mathématiques</a> dont l'objet est l'étude des opérations algébriques (<a href="/wiki/Addition" title="Addition">addition</a>, <a href="/wiki/Multiplication" title="Multiplication">multiplication</a>, <a href="/wiki/Soustraction" title="Soustraction">soustraction</a>, <a href="/wiki/Division" title="Division">division</a> et <a href="/wiki/Racine_d%27un_nombre" title="Racine d'un nombre">extraction de racine</a>) sur les nombres <a href="/wiki/Nombre_r%C3%A9el" title="Nombre réel">réels</a> ou <a href="/wiki/Nombre_complexe" title="Nombre complexe">complexes</a>, et dont l'objectif principal est la résolution d'<a href="/wiki/%C3%89quation_polynomiale" title="Équation polynomiale">équations polynomiales</a>. </p><p>Le qualificatif d'<i>élémentaire</i> (ou <i>classique</i>) est destiné à la différencier de l'<a href="/wiki/Alg%C3%A8bre_g%C3%A9n%C3%A9rale" title="Algèbre générale">algèbre <i>générale</i></a> (ou <i>moderne</i>), qui étudie les <a href="/wiki/Structure_alg%C3%A9brique" title="Structure algébrique">structures algébriques</a> (<a href="/wiki/Groupe_(math%C3%A9matiques)" title="Groupe (mathématiques)">groupes</a>, <a href="/wiki/Corps_commutatif" title="Corps commutatif">corps commutatifs</a>, etc.) généralisant les notions de <a href="/wiki/Nombre" title="Nombre">nombre</a> et d'<a href="/wiki/Op%C3%A9ration_(math%C3%A9matiques)" title="Opération (mathématiques)">opération</a>. Elle se différencie également de l'<a href="/wiki/Arithm%C3%A9tique_%C3%A9l%C3%A9mentaire" title="Arithmétique élémentaire">arithmétique élémentaire</a> par l'usage de lettres pour représenter les <a href="/wiki/Inconnue_(math%C3%A9matiques)" title="Inconnue (mathématiques)">nombres inconnus</a>. </p><p>En ce sens, l'adjectif <b>algébrique</b> peut, suivant les cas, être un synonyme de <i><a href="/wiki/Polyn%C3%B4me" title="Polynôme">polynomial</a></i> (comme dans <i><a href="/wiki/Courbe_alg%C3%A9brique" title="Courbe algébrique">courbe algébrique</a></i>) ou l'antonyme d'<i><a href="/wiki/Arithm%C3%A9tique_%C3%A9l%C3%A9mentaire" title="Arithmétique élémentaire">arithmétique</a></i>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Expressions_algébriques"><span id="Expressions_alg.C3.A9briques"></span>Expressions algébriques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alg%C3%A8bre_classique&veaction=edit&section=1" title="Modifier la section : Expressions algébriques" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alg%C3%A8bre_classique&action=edit&section=1" title="Modifier le code source de la section : Expressions algébriques"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Une expression algébrique est constituée de nombres, de lettres et de signes opératoires : </p> <ul><li>le signe <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle +}"></span> est utilisé pour marquer l'<a href="/wiki/Addition" title="Addition">addition</a>.</li> <li>le signe <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04bd52ce670743d3b61bec928a7ec9f47309eb36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle -}"></span> est utilisé pour marquer la <a href="/wiki/Soustraction" title="Soustraction">soustraction</a>.</li> <li>les signes <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span> ou <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cdot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⋅</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cdot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba2c023bad1bd39ed49080f729cbf26bc448c9ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.439ex; margin-bottom: -0.61ex; width:0.647ex; height:1.176ex;" alt="{\displaystyle \cdot }"></span> sont utilisés pour marquer la <a href="/wiki/Multiplication" title="Multiplication">multiplication</a>. Quand la multiplication concerne deux lettres, il est possible d'écrire <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ab}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49337c5cf256196e2292f7047cb5da68c24ca95d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.227ex; height:2.176ex;" alt="{\displaystyle ab}"></span> au lieu de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\times b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>×</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\times b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b420244850c1a22be4c326f91e146db8b037f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.068ex; height:2.176ex;" alt="{\displaystyle a\times b}"></span>.</li> <li>le signe <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \div }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>÷</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \div }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/837b35ee5d25b5ce7b07f292c27cc90533dd9fd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle \div }"></span> est utilisé pour marquer la <a href="/wiki/Division" title="Division">division</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\div b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>÷</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\div b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/021958e4ad3e896d02f70c725544ad3fac40727c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.068ex; height:2.176ex;" alt="{\displaystyle a\div b}"></span> pouvant également s'écrire <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\cfrac {a}{b}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\cfrac {a}{b}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a27bd209f0174f712484ea6a3f07c12cf482e4bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:2.066ex; height:7.176ex;" alt="{\displaystyle {\cfrac {a}{b}}}"></span>.</li></ul> <p>Par exemple : </p> <ul><li>Le produit d'un nombre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> augmenté de 3 par lui-même s'écrit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x+3)x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x+3)x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/344288c9f9e93b69648c4e6fca79f03a9f731318" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.472ex; height:2.843ex;" alt="{\displaystyle (x+3)x}"></span>.</li> <li>La différence des carrés de deux nombres <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> s'écrit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}-b^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}-b^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d889199ccf9e44b772541baebe35e97744002f2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.176ex; height:2.843ex;" alt="{\displaystyle a^{2}-b^{2}}"></span></li></ul> <p>Évaluer une expression algébrique consiste à attribuer une valeur à chacune des variables, puis à effectuer le calcul arithmétique obtenu. </p><p>Par exemple évaluer l'expression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+x-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+x-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3aff20f375d1f7f76c6fb254b07701450fb454cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.557ex; height:2.843ex;" alt="{\displaystyle x^{2}+x-1}"></span> pour <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f39b6e42e5ffb81ac7b051b9e48b9a91d0713c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle x=2}"></span> consiste à effectuer le calcul <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{2}+2-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{2}+2-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46896e2253dd7cd298ece6c14b40dd88557de36a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.222ex; height:2.843ex;" alt="{\displaystyle 2^{2}+2-1}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Propriétés_de_l'addition"><span id="Propri.C3.A9t.C3.A9s_de_l.27addition"></span>Propriétés de l'addition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alg%C3%A8bre_classique&veaction=edit&section=2" title="Modifier la section : Propriétés de l'addition" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alg%C3%A8bre_classique&action=edit&section=2" title="Modifier le code source de la section : Propriétés de l'addition"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'addition : </p> <ul><li>s'écrit <i>a</i> + <i>b</i> ;</li> <li>est <a href="/wiki/Commutativit%C3%A9" class="mw-redirect" title="Commutativité">commutative</a> : <i>a</i> + <i>b</i> = <i>b</i> + <i>a</i> ;</li> <li>est <a href="/wiki/Associative" class="mw-redirect" title="Associative">associative</a> : (<i>a</i> + <i>b</i>) + <i>c</i> = <i>a</i> + (<i>b</i> + <i>c</i>) ;</li> <li>a une <a href="/wiki/Application_r%C3%A9ciproque" class="mw-redirect" title="Application réciproque">application réciproque</a> appelée soustraction : (<i>a</i> + <i>b</i>) − <i>b</i> = <i>a</i>, équivaut à additionner un nombre négatif, <i>a</i> − <i>b</i> = <i>a</i> + (−<i>b</i>) ;</li> <li>a un <a href="/wiki/%C3%89l%C3%A9ment_neutre" title="Élément neutre">élément neutre</a> 0 qui conserve le nombre : <i>a</i> + 0 = <i>a</i>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Propriétés_de_la_multiplication"><span id="Propri.C3.A9t.C3.A9s_de_la_multiplication"></span>Propriétés de la multiplication</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alg%C3%A8bre_classique&veaction=edit&section=3" title="Modifier la section : Propriétés de la multiplication" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alg%C3%A8bre_classique&action=edit&section=3" title="Modifier le code source de la section : Propriétés de la multiplication"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La multiplication : </p> <ul><li>s'écrit <i>a</i> × <i>b</i> ou <i>a</i> • <i>b</i> ;</li> <li>est <a href="/wiki/Commutativit%C3%A9" class="mw-redirect" title="Commutativité">commutative</a> : <i>a</i> × <i>b</i> = <i>b</i> × <i>a</i> ;</li> <li>est <a href="/wiki/Associative" class="mw-redirect" title="Associative">associative</a> : (<i>a</i> × <i>b</i>) × <i>c</i> = <i>a</i> × (<i>b</i> × <i>c</i>) ;</li> <li>est abrégé par la juxtaposition : <i>a</i> × <i>b</i> ≡ <i>ab</i> ;</li> <li>a un <a href="/wiki/%C3%89l%C3%A9ment_neutre" title="Élément neutre">élément neutre</a> 1 qui conserve le nombre : <i>a</i> × 1 = <i>a</i> ;</li> <li>pour les nombres différents de <a href="/wiki/Z%C3%A9ro" title="Zéro">zéro</a>, a une <a href="/wiki/Application_r%C3%A9ciproque" class="mw-redirect" title="Application réciproque">application réciproque</a> appelée division : (<i>ab</i>)/<i>b</i> = <i>a</i>, équivaut à multiplier par son <a href="/wiki/Inverse" title="Inverse">inverse</a>, <i>a</i>/<i>b</i> = <i>a</i>(1/<i>b</i>) ;</li> <li>est <a href="/wiki/Distributivit%C3%A9" title="Distributivité">distributive</a> par rapport à l'addition : (<i>a</i> + <i>b</i>)<i>c</i> = <i>ac</i> + <i>bc</i> ;</li> <li>a un <a href="/wiki/%C3%89l%C3%A9ment_absorbant" title="Élément absorbant">élément absorbant</a> 0 qui annule le nombre : <i>a</i> × 0 = 0.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Factorisation_et_développement"><span id="Factorisation_et_d.C3.A9veloppement"></span>Factorisation et développement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alg%C3%A8bre_classique&veaction=edit&section=4" title="Modifier la section : Factorisation et développement" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alg%C3%A8bre_classique&action=edit&section=4" title="Modifier le code source de la section : Factorisation et développement"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Factoriser une expression algébrique, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span>, consiste à en transformer l'écriture sous la forme d'un produit de deux ou plusieurs expressions (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>, ...) : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=A\times B\times \cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>A</mi> <mo>×</mo> <mi>B</mi> <mo>×</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=A\times B\times \cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d5dde6c7b8144ddf1972c53b54d9ae633654cf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.785ex; height:2.176ex;" alt="{\displaystyle E=A\times B\times \cdots }"></span></center> <p>Chacune des expressions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>, ... est appelée un facteur. </p><p>Développer une expression algébrique, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span>, consiste à en transformer l'écriture sous la forme d'une somme (ou différence) de deux ou plusieurs expressions. (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>, ...) : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=A+B+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=A+B+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba016a8a06493832d83e5b3184f8ae3b9ba2506" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:16.785ex; height:2.343ex;" alt="{\displaystyle E=A+B+\cdots }"></span></center> <p>Chacune des expressions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>, ... est appelée un terme. </p> <div class="mw-heading mw-heading2"><h2 id="Bibliographie">Bibliographie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alg%C3%A8bre_classique&veaction=edit&section=5" title="Modifier la section : Bibliographie" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alg%C3%A8bre_classique&action=edit&section=5" title="Modifier le code source de la section : Bibliographie"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ouvrages">Ouvrages</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alg%C3%A8bre_classique&veaction=edit&section=6" title="Modifier la section : Ouvrages" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alg%C3%A8bre_classique&action=edit&section=6" title="Modifier le code source de la section : Ouvrages"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="ouvrage" id="DahanPeiffer"><a href="/wiki/Amy_Dahan" title="Amy Dahan">A. <span class="nom_auteur">Dahan-Dalmedico</span></a> et <a href="/wiki/Jeanne_Peiffer" title="Jeanne Peiffer">J. Peiffer</a>, <cite class="italique">Une histoire des mathématiques : Routes et dédales</cite>, <time>1986</time> <small>[<a href="/wiki/R%C3%A9f%C3%A9rence:Histoire_des_math%C3%A9matiques_(Dahan-Dalmedico,_Peiffer)" title="Référence:Histoire des mathématiques (Dahan-Dalmedico, Peiffer)">détail des éditions</a>]</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Une+histoire+des+math%C3%A9matiques&rft.stitle=Routes+et+d%C3%A9dales&rft.aulast=Dahan-Dalmedico&rft.aufirst=A.&rft.au=J.+Peiffer&rft.date=1986&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAlg%C3%A8bre+classique"></span></span></li> <li><span class="ouvrage" id="Djebbar2005"><span class="ouvrage" id="Ahmed_Djebbar2005"><a href="/wiki/Ahmed_Djebbar" title="Ahmed Djebbar">Ahmed Djebbar</a> (<abbr class="abbr" title="préface">préf.</abbr> <a href="/wiki/Bernard_Maitte" title="Bernard Maitte">Bernard Maitte</a>), <cite class="italique">L'algèbre arabe, genèse d'un art</cite>, Vuibert/Adapt, <time>2005</time>, 214 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/2711753816" title="Spécial:Ouvrages de référence/2711753816"><span class="nowrap">2711753816</span></a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=L%27alg%C3%A8bre+arabe%2C+gen%C3%A8se+d%27un+art&rft.pub=Vuibert%2FAdapt&rft.aulast=Djebbar&rft.aufirst=Ahmed&rft.date=2005&rft.tpages=214&rft.isbn=2711753816&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAlg%C3%A8bre+classique"></span></span></span> — Tour d'horizon de l'algèbre arabe, des origines au <a href="/wiki/XVe_si%C3%A8cle" title="XVe siècle"><abbr class="abbr" title="15ᵉ siècle"><span class="romain">XV</span><sup style="font-size:72%">e</sup></abbr> siècle</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Articles_d'encyclopédies"><span id="Articles_d.27encyclop.C3.A9dies"></span>Articles d'encyclopédies</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alg%C3%A8bre_classique&veaction=edit&section=7" title="Modifier la section : Articles d'encyclopédies" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alg%C3%A8bre_classique&action=edit&section=7" title="Modifier le code source de la section : Articles d'encyclopédies"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="ouvrage" id="MerzlyakovShirshov2001"><span class="ouvrage" id="Yu._I._MerzlyakovA.I._Shirshov2001"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Yu. I. <span class="nom_auteur">Merzlyakov</span> et A.I. <span class="nom_auteur">Shirshov</span>, « <cite style="font-style:normal" lang="en">Algebra</cite> », <i><span class="lang-en" lang="en">Encyclopaedia of Mathematics</span></i>, Springer,‎ <time>2001</time> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/1402006098" title="Spécial:Ouvrages de référence/1402006098"><span class="nowrap">1402006098</span></a>, <a rel="nofollow" class="external text" href="http://eom.springer.de/A/a011340.htm">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Algebra&rft.jtitle=Encyclopaedia+of+Mathematics&rft.aulast=Merzlyakov&rft.aufirst=Yu.+I.&rft.au=Shirshov%2C+A.I.&rft.date=2001&rft.isbn=1402006098&rft_id=http%3A%2F%2Feom.springer.de%2FA%2Fa011340.htm&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAlg%C3%A8bre+classique"></span></span></span></li> <li>« Algèbre », dans Encyclopédie Larousse, <small>[<a rel="nofollow" class="external text" href="http://www.larousse.fr/encyclopedie/nom-commun-nom/alg%C3%A8bre_nf_Branche_des_math%C3%A9matiques_qui,_dans_sa_partie_classique,_se_consacre_%C3%A0/19868">lire en ligne</a>]</small></li> <li><span class="ouvrage" id="Baruk"><span class="ouvrage" id="Stella_Baruk"><a href="/wiki/Stella_Baruk" title="Stella Baruk">Stella <span class="nom_auteur">Baruk</span></a>, <cite style="font-style:normal">« Algèbre »</cite>, dans <cite class="italique">Dictionnaire de mathématiques élémentaires</cite> <small>[<a href="/wiki/R%C3%A9f%C3%A9rence:Dictionnaire_de_math%C3%A9matiques_%C3%A9l%C3%A9mentaires_(Baruk)" title="Référence:Dictionnaire de mathématiques élémentaires (Baruk)">détail des éditions</a>]</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.btitle=Dictionnaire+de+math%C3%A9matiques+%C3%A9l%C3%A9mentaires&rft.atitle=Alg%C3%A8bre&rft.aulast=Baruk&rft.aufirst=Stella&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAlg%C3%A8bre+classique"></span></span></span>, § Algèbre classique.</li></ul> <ul><li><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Cet article est partiellement ou en totalité issu de l’article de Wikipédia en anglais intitulé <span class="plainlinks">« <a class="external text" href="https://en.wikipedia.org/wiki/Elementary_algebra?oldid=299529603">Elementary algebra</a> » <small>(<a class="external text" href="https://en.wikipedia.org/wiki/Elementary_algebra?action=history">voir la liste des auteurs</a>)</small></span>.</li></ul> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer" typeof="mw:File"><a href="/wiki/Portail:Alg%C3%A8bre" title="Portail de l’algèbre"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/24px-Arithmetic_symbols.svg.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/36px-Arithmetic_symbols.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/48px-Arithmetic_symbols.svg.png 2x" data-file-width="210" data-file-height="210" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Alg%C3%A8bre" title="Portail:Algèbre">Portail de l’algèbre</a></span> </span></li> </ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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