Mathematical Operations on Algebraic Expressions - Algebraic Expressions and Identities

<!DOCTYPE html>    <html lang="en-US" prefix="og: http://ogp.me/ns#" >  <head> <meta charset="UTF-8" /> <meta name="keywords" content="Data Structures,Algorithms,Python,Java,C,C++,JavaScript,Android Development,SQL,Data Science,Machine Learning,PHP,Web Development,System Design,Tutorial,Technical Blogs,Interview Experience,Interview Preparation,Programming,Competitive Programming,Jobs,Coding Contests,GATE CSE,HTML,CSS,React,NodeJS,Placement,Aptitude,Quiz,Computer Science,Programming Examples,GeeksforGeeks Courses,Puzzles,SSC,Banking,UPSC,Commerce,Finance,CBSE,School,k12,General Knowledge,News,Mathematics,Exams" /> <meta name="viewport" content="width=device-width, initial-scale=1.0, minimum-scale=0.5, maximum-scale=3.0"> <link rel="shortcut icon" href="https://media.geeksforgeeks.org/wp-content/cdn-uploads/gfg_favicon.png" type="image/x-icon" /> <link rel="preconnect" href="https://fonts.googleapis.com"> <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin> <meta name="theme-color" content="#308D46" /> <meta name='robots' content='index, follow, max-image-preview:large, max-snippet:-1' /> <meta name="image" property="og:image" content="https://media.geeksforgeeks.org/wp-content/cdn-uploads/gfg_200x200-min.png"> <meta property="og:image:type" content="image/png"> <meta property="og:image:width" content="200"> <meta property="og:image:height" content="200"> <meta name="facebook-domain-verification" content="xo7t4ve2wn3ywfkjdvwbrk01pvdond" /> <script src="https://cdnads.geeksforgeeks.org/synchronously_gfg_ads.min.js"></script> <script defer src="https://apis.google.com/js/platform.js"></script> <script src="//cdnjs.cloudflare.com/ajax/libs/require.js/2.1.14/require.min.js"></script>     <script> var IHPWT={}; //Initialize Namespace var pbjs = pbjs || {}; pbjs.que = pbjs.que || []; var googletag = googletag || {}; googletag.cmd = googletag.cmd || []; var gptRan = false; </script> <script defer src="https://ads.pubmatic.com/AdServer/js/pwt/162080/12331/pwt.js"></script> <script defer src="https://securepubads.g.doubleclick.net/tag/js/gpt.js"></script> <script defer src="https://cdnads.geeksforgeeks.org/prebid.js?ver=0.1"></script> <script defer src="https://cdnads.geeksforgeeks.org/gfg_ads.min.js?ver=0.1"></script>  <title>Mathematical Operations on Algebraic Expressions - Algebraic Expressions and Identities | Class 8 Maths - GeeksforGeeks</title> <link rel="profile" href="http://gmpg.org/xfn/11" /> <link rel="pingback" href="" />     <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "Article", "mainEntityOfPage": { "@type": "WebPage", "id": "https://www.geeksforgeeks.org/mathematical-operations-on-algebraic-expressions-algebraic-expressions-and-identities-class-8-maths/" }, "headline": "Mathematical Operations on Algebraic Expressions Algebraic Expressions and Identities | Class 8 Maths", "datePublished": "2020-11-16 12:59:09", "dateModified": "2020-11-17 05:34:12", "image": { "@type": "ImageObject", "url": "https://media.geeksforgeeks.org/wp-content/uploads/gfg_200X200-100x100.png", "width": "100", "height": "100" }, "author": { "@type": "Organization", "name": "GeeksforGeeks", "url": "https://www.geeksforgeeks.org/", "logo": { "@type": "ImageObject", "url": "https://media.geeksforgeeks.org/wp-content/cdn-uploads/logo-new-2.svg", "width": "301", "height": "40" } }, "publisher": { "@type": "Organization", "name": "GeeksforGeeks", "url": "https://www.geeksforgeeks.org/", "logo": { "@type": "ImageObject", "url": "https://media.geeksforgeeks.org/wp-content/cdn-uploads/logo-new-2.svg", "width": "301", "height": "40" } }, "description": "The basic operations that are being used in mathematics (especially in real number systems) are addition, subtraction, multiplication and so on. These operations can also be done on the algebraic expressions. Let us see them in detail. Algebraic expressions (also known as algebraic equations) are defined as \"the type of", "about": [ { "@type": "Thing", "name": "TechnicalScripter" }, { "@type": "Thing", "name": "Picked" }, { "@type": "Thing", "name": "Maths" }, { "@type": "Thing", "name": "SchoolLearning" }, { "@type": "Thing", "name": "Class8" }, { "@type": "Thing", "name": "TechnicalScripter2020" }, { "@type": "Thing", "name": "Algebra" }, { "@type": "Thing", "name": "MathsClass8" } ] }</script> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "WebSite", "url": "https://www.geeksforgeeks.org/", "potentialAction": { "@type": "SearchAction", "target": "https://www.geeksforgeeks.org/search/{search_term_string}/", "query-input": "required name=search_term_string" } }</script> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "Organization", "name": "GeeksforGeeks", "url": "https://www.geeksforgeeks.org/", "logo": "https://media.geeksforgeeks.org/wp-content/cdn-uploads/20200817185016/gfg_complete_logo_2x-min.png", "description": "A computer science portal for geeks. 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alt="News"></img> <span class='kebab_menu_news_text'>Follow</span> </a> </div> </div> </div> <div class="text"> <p>The basic operations that are being used in mathematics (especially in real number systems) are addition, subtraction, multiplication and so on. These operations can also be done on the algebraic expressions. Let us see them in detail.</p> <p>Algebraic expressions (also known as <strong>algebraic equations</strong>) are defined as “the type of expressions”, in which it mainly consists of three parts namely,</p><div id="GFG_AD_gfg_mobile_336x280" style="margin: 5px 0;"></div> <blockquote> <p><i><strong>Variables:</strong> Alphabetical letters which are associated with some integers.</i></p> <p><i><strong>Coefficients: </strong>The values (integers) that are associated with the variables.</i></p> <p><i><strong>Constants:</strong> Only the integers which are associated with the expressions.</i></p> </blockquote> <p><strong>Example: </strong>25x + 16y+ 9, 2y2 – 3y, 2a + 3b + c, etc.</p> <blockquote> <p><i><strong>Note: All the Coefficients, Variables and Constants are associated with each other by various types of arithmetic operators.</strong></i></p> </blockquote> <p> The algebraic expressions are classified into three types, namely,</p> <ol> <li>Monomial or single variable expressions.</li> <li>Binomial or two variable expressions.</li> <li>Polynomial or multi variable expressions.</li> </ol> <h2><strong>Mathematical Operations on Algebraic Expressions</strong></h2> <h3><strong>Addition of Algebraic Expressions</strong></h3> <p>Addition of algebraic expressions involves the following steps:</p> <p><strong>Step 1:</strong> Group all the like terms based on the coefficients, (i.e.) the coefficients consisting of the same variables are grouped together.</p> <p><strong>Step 2: </strong>All the grouped coefficient under the same variables should be performed <strong>ADDITION OPERATION (+) </strong>and should be written as a single coefficient term with its respective coefficient.</p><div id="GFG_AD_Desktop_InContent_ATF_336x280" style="text-align:center; max-height: 280px;"></div><div id="GFG_AD_gfg_mobile_336x280_1" style="margin: 5px 0;"></div> <p><strong>Step 3:</strong> Similarly, for all the like variables, the operations are needed to be done.</p><div id="_GFG_ABP_Incontent_728x90" style="text-align:center;"></div> <p><strong>Step 4:</strong> For constants, add them and no need to include any variables.</p> <p><strong>Step 5:</strong> If there not exists any like term for any term, keep it as it is.</p> <p><strong>Example:</strong></p> <blockquote> <p><i>Let us take an example, consider we are adding two algebraic expressions,</i></p> <p><i>5x + 6y + 7z and 6x – 7y + 3</i></p> <p><i>Now let us group the like terms,</i></p> <p><i>5x + 6x + 6y – 7y + 7z + 3</i></p> <p><i>Now let us perform + operation on like terms and the result will be, </i></p> <p><i>x coefficient: 6 + 5 = 11</i></p> <p><i>y coefficient: 6 – 7 = -1</i></p> <p><i>z coefficient: 7</i></p> <p><i>Constant: 3</i></p> <p><i> So , the result is 11x – y + 7z + 3 .</i></p> <p><i>Similarly, for another example,</i></p> <p><i>9a + 7c and </i></p> <p><i>19b + 4</i></p> <p><i>The result is 9a + 19b + 7c + 4</i></p> </blockquote> <blockquote> <p><i><strong>Note:</strong> The addition operation can be done on any number of Algebraic Equations, not limited to only adding two expressions.</i></p> </blockquote> <h3><strong>Subtraction of Algebraic Expressions</strong></h3> <p>The subtraction of the algebraic expressions is very similar to the addition of the expressions. Though, it is recommended to use the <strong>Column Subtraction Method.</strong></p> <p>The following process is to be followed for the subtraction of algebraic expressions:</p><div style="text-align:center;margin:20px 0; max-height: 280px;" id="GFG_AD_gfg_outstream_incontent"></div> <p><strong>Step 1:</strong> Write the algebraic expressions line by line, one after other (newline).</p> <p><strong>Step 2:</strong> Group the like terms based on the variables, and they are needed to write the expressions in the same order of variables for all expressions.</p> <p><strong>Step 3:</strong> Toggle the sign of all the terms in the last expression that has been written (i.e.) Change + to – and – to +.</p> <p><strong>Step 4:</strong> Then perform the necessary operation for the expressions.</p> <p><strong>Step 5: </strong>It is recommended to solve a couple of expressions one by one if there are any number of algebraic equations to be solved.</p> <p><strong>Example:</strong></p> <blockquote> <p><i>Let us consider an example of two algebraic expressions to be solved,</i></p> <p><i>5x – 7y + 9 and 8y + 7x – 1 </i></p> <p><i>Now let us group the like terms and solve them,</i></p> <p><i>5x – 7y + 9 </i></p> <p><i>7x + 8y -1</i></p> <p><i>Now let us toggle the sign of the last written expression by order,</i></p> <p><i>5x – 7y + 9</i></p> <p><i>(-)7x (-)8y (+)1</i></p> <p><i>( ) represents the toggled sign.</i></p> <p><i>Now the result would be,</i></p> <p><i>x coefficient: 5 – 7 = -2</i></p> <p><i>y coefficient:  -7 – 8 = -15</i></p> <p><i>constant: 9 + 1 = 10</i></p> <p><i>Therefore, the result is -2x – 15y + 10</i></p> <p><i>Now, let us consider another example,</i></p> <p><i>6a – 7b – 1 and 4a – 6b – 1</i></p> <p><i>The result is 2a – b (No constant because they cancel each other)</i></p> </blockquote> <h3><strong>Multiplication of Algebraic Expressions</strong></h3> <p>Multiplication is one of the frequent arithmetic operations that is been done on the algebraic expressions/equations. The following process can be followed to multiply a set of algebraic expressions,</p> <p><strong>Step 1: </strong>The multiplication is done by taking each and every term of the first expression and multiplying with each and every term of the second expression.</p> <p><strong>Step 2:</strong> While multiplying if the same variables exist, then add the powers <strong>(by PRODUCT RULE) </strong>and to be written as exponent with the variable.</p> <p><strong>Step 3:</strong> If different variables exist, then just write them as the product along with another variable.</p> <p><strong>Step 4:</strong> Then for multiplying coefficients, like signs will give a POSITIVE result and unlike signs will give a NEGATIVE result.</p> <p><strong>Step 5:</strong> Each and every term obtain after multiplication should be separated by their respective signs.</p> <p><strong>Example:</strong></p> <blockquote> <p><i>Let us see an example for multiplication of algebraic expressions,</i></p> <p><i>5x + 6y and </i><span style="background-color:rgb(250,250,250);color:rgba(0,0,0,0.87);"><i>9</i></span><i>x + 9y</i></p> <p><i>Here, 5x to be multiplied with second equation and 6y to be multiplied with second equation.</i></p> <p><i>Now take the first term of the first expression and multiply with each and every term of the second expression by following the steps mentioned above.</i></p> <p><i>(5x * 9x) + (5x * 9y) = 45x<sup>2</sup> + 45xy</i></p> <p><i>Similarly, for second term,</i></p> <p><i>(6y * 9x) + (6y * 9y) = 54xy + 54y<sup>2</sup></i></p> <p><i>Now the result would be combining them,</i></p> <p><i>45x<sup>2</sup> + 45xy + 54xy + 54y<sup>2 </sup></i></p> <p><i>Similarly, consider other examples,</i></p> <p><i>4x and 6x – 8y + 2z</i></p> <p><i>The result is 24x<sup>2</sup> – 32xy + 8xz</i></p> </blockquote> <div class='article_bottom_text'></div><br> <div id="video-tab-content" class="video-tab-content"> <div style="text-align: center; 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Let's learn about Square, including its properties, area, perimeter, examples,</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 4: Practical Geometry <span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/construction-of-a-quadrilateral/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Construction of a Quadrilateral </div> <div class="gfg-similar-read-item-subheading">It is famously said that Geometry is the knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them. Practical geometry is an important branch of geometry that helps us to study the size, positions, shapes as well as dimensions of objects and draw them wi</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 5: Data Handling<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/data-handling/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Data Handling </div> <div class="gfg-similar-read-item-subheading">Data Handling: Nowadays, managing and representing data systematically has become very important especially when the data provided is large and complex, This is when Data Handling comes into the picture. Data handling involves the proper management of research data throughout and beyond the lifespan</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">12 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/what-is-data-organization/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">What is Data Organization? </div> <div class="gfg-similar-read-item-subheading">It is a critical process that involves structuring, categorizing, and managing data to make it more accessible, usable, and analyzable. Whether in research, business, or everyday applications, well-organized data can significantly enhance efficiency and decision-making. The importance of data organi</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">10 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/frequency-distribution/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Frequency Distribution - Table, Graphs, Formula </div> <div class="gfg-similar-read-item-subheading">Frequency Distribution is a tool in statistics that helps us organize the data and also helps us reach meaningful conclusions. It tells us how often any specific values occur in the dataset. A frequency distribution in a tabular form organizes data by showing the frequencies (the number of times val</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">12 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/pie-charts/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Pie Chart </div> <div class="gfg-similar-read-item-subheading">Pie chart is a popular and visually intuitive tool used in data representation, making complex information easier to understand at a glance. This circular graph divides data into slices, each representing a proportion of the whole, allowing for a clear comparison of different categories making it ea</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">13 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/chance-and-probability/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Chance and Probability </div> <div class="gfg-similar-read-item-subheading">Chance is defined as the natural occurrence of any event without any interference, we can also say that the possibility of any event is the chance of the event, and mathematically we define the chance as the probability of an event. Probability refers to the likelihood of the occurrence of an event.</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/random-experiment-probability/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Random Experiment - Probability </div> <div class="gfg-similar-read-item-subheading">In a cricket match, before the game begins. Two captains go for a toss. Tossing is an activity of flipping a coin and checking the result as either “Head” or “Tail”. Similarly, tossing a die gives us a number from 1 to 6. All these activities are examples of experiments. An activity that gives us a</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">12 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/probability-in-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Probability in Maths </div> <div class="gfg-similar-read-item-subheading">Probability is a field of mathematics that deals with events and quantifies their likelihood of occurring with numerical values ranging from 0 to 1. Higher probabilities indicate a greater chance of the event happening. It is mainly a ratio between the given event and the total number of events. Wha</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">3 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 6: Squares and Square Roots<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/squares-and-square-roots/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Squares and Square Roots </div> <div class="gfg-similar-read-item-subheading">Squares and Square roots are highly used mathematical concepts which are used for various purposes. Squares are numbers produced by multiplying a number by itself. Conversely, the square root of a number is the value that, when multiplied by itself, results in the original number. Thus, squaring and</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">13 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/how-to-find-square-root-of-a-number/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">How to Find Square Root of a Number? </div> <div class="gfg-similar-read-item-subheading">In everyday situations, the challenge of calculating the square root of a number is faced. What if one doesn't have access to a calculator or any other gadget? It can be done with old-fashioned paper and pencil in a long-division style. Yes, there are a variety of ways to do so. Let's start with dis</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">13 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/pythagorean-triples/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Pythagorean Triples </div> <div class="gfg-similar-read-item-subheading">Pythagorean triples are sets of three positive integers that satisfy the Pythagorean Theorem. This ancient theorem, attributed to the Greek mathematician Pythagoras, is fundamental in geometry and trigonometry. The theorem states that in any right-angled triangle, the square of the length of the hyp</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">14 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 7: Cubes and Cube Roots <span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/cube-roots/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Cube Roots </div> <div class="gfg-similar-read-item-subheading">A cube root of a number a is a value b such that when multiplied by itself three times (i.e., [Tex]b \times b \times b[/Tex]), it equals a. Mathematically, this is expressed as: b3 = a, where a is the cube of b. Cube is a number that we get after multiplying a number 3 times by itself. For example,</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/perfect-cube/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Perfect Cube </div> <div class="gfg-similar-read-item-subheading">Given a number N, the task is to check whether the given number N is a perfect cube or not. Examples: Input: N = 216 Output: Yes Explanation: As 216 = 6*6*6. Therefore the cube root of 216 is 6. Input: N = 100 Output: No Table of Content Naive Approach:Using Build-in Functions: Using Prime Factors :</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">15+ min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 8: Comparing Quantities<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/ratios-and-percentages/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Ratios and Percentages </div> <div class="gfg-similar-read-item-subheading">Ratios and Percentages: Comparing quantities is easy, each of the quantities is defined to a specific standard and then the comparison between them takes place after that. Comparing quantities can be effectively done by bringing them to a certain standard and then comparing them related to that spec</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/fractions/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Fractions - Definition, Types & Examples </div> <div class="gfg-similar-read-item-subheading">Fractions are numerical expressions used to represent parts of a whole or ratios between quantities. They consist of two numbers separated by a horizontal line, where the number above the line is called the numerator and the number below the line is called the denominator. Example, If A pizza is div</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/percentage/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Percentage </div> <div class="gfg-similar-read-item-subheading">Percentage: In mathematics, a percentage is a figure or ratio that signifies a fraction out of 100. It is a method used to express a dimensionless relationship between two numbers, similar to ratios, fractions, and decimals. Percentages are commonly indicated by the symbol "%" following the number.</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">13 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/discount-formula/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Discount Formula </div> <div class="gfg-similar-read-item-subheading">Discount in Mathematics is defined as the reduction in price of any service and product. Discount is offered by the business owner to easily and quickly sell their product or services. Giving discounts increases the sales of the business and helps the business retain its customer. Discount is always</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/sales-tax-value-added-tax-and-goods-and-services-tax-comparing-quantities-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Sales Tax, Value Added Tax, and Goods and Services Tax - Comparing Quantities | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">Tax is a mandatory fee levied by the government to collect revenue for public works providing the best facilities and infrastructure. The first known Tax system was in Ancient Egypt around 3000–2800 BC, in First Dynasty of Egypt. The first form of taxation was corvée and tithe. In India, The Tax was</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">6 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/simple-interest/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Simple Interest </div> <div class="gfg-similar-read-item-subheading">Simple interest is a method used to determine the interest amount on a principal sum based on a specified interest rate and duration of time. Simple interest is a widely used concept across various industries, including banking, finance, and automotive sectors. It serves as a fundamental method for</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">8 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/compound-interest-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Compound Interest | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">Compound Interest: Compounding is a process of re-investing the earnings in your principal to get an exponential return as the next growth is on a bigger principal, following this process of adding earnings to the principal. In this passage of time, the principal will grow exponentially and produce</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/compound-interest-formula/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Compound Interest Formula </div> <div class="gfg-similar-read-item-subheading">Compound Interest is the interest that is calculated against a loan or deposit amount in which interest is calculated for the principal as well as the previous interest earned. The common difference between compound and simple interest is that in compound interest, interest is calculated for the pri</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">15 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown" style="background-color:var(--leftbar-background-color); border-bottom:1px solid #CCC;"><h2 class="dropdown-title active">Chapter 9: Algebraic Expressions and Identities <span class="gfg-icon gfg-icon_arrow-down-thin upside"></span></h2><ul><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/algebraic-expressions-and-identities-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Algebraic Expressions and Identities </div> <div class="gfg-similar-read-item-subheading">An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations, representing a value without an equality sign. Whereas, algebraic identities are equations that hold true for all values of the variables involved. Learning different algebraic identities is crucial</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/types-of-polynomials/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Types of Polynomials (Based on Terms and Degrees) </div> <div class="gfg-similar-read-item-subheading">Types of Polynomials: In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations. There are mainly four types of polynomials based on degree-constant polynomial (zero degree), linear polynomial ( 1st degree), quadratic polynomial (2n</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/like-and-unlike-algebraic-terms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Like and Unlike Algebraic Terms: Definition and Examples </div> <div class="gfg-similar-read-item-subheading">Like terms are terms in algebraic expressions that have the same variables raised to the same powers. Like and Unlike Terms are the types of terms in algebra, and we can differentiate between like and unlike terms by simply checking the variables and their powers. We define algebraic terms as the in</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="currentpage similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/mathematical-operations-on-algebraic-expressions-algebraic-expressions-and-identities-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Mathematical Operations on Algebraic Expressions - Algebraic Expressions and Identities | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">The basic operations that are being used in mathematics (especially in real number systems) are addition, subtraction, multiplication and so on. These operations can also be done on the algebraic expressions. Let us see them in detail. Algebraic expressions (also known as algebraic equations) are de</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">5 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/multiplying-polynomials/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Multiplying Polynomials </div> <div class="gfg-similar-read-item-subheading">Multiplying Polynomials is a process of multiplication of various Polynomials and finding their product. Multiplication is the fundamental operation and it can be performed on polynomials, Multiplication of polynomials is achieved by multiplying the coefficients of polynomials with each other and va</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/standard-algebraic-identities-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Standard Algebraic Identities </div> <div class="gfg-similar-read-item-subheading">Algebraic Identities are algebraic equations that are always true for every value of the variable in them. The algebraic equations that are valid for all values of variables in them are called algebraic identities. It is used for the factorization of polynomials. In this way, algebraic identities ar</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 10: Visualising Solid Shapes<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/visualizing-solid-shapes/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Visualizing Solid Shapes </div> <div class="gfg-similar-read-item-subheading">Visualizing Solid Shapes: Any plane or any shape has two measurements length and width, which is why it is called a two-dimensional(2D) object. Circles, squares, triangles, rectangles, trapeziums, etc. are 2-D shapes. If an object has length, width, and breadth then it is a three-dimensional object(</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">8 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/mapping-space-around-us-visualizing-solid-shapes-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Mapping Space Around Us - Visualizing Solid Shapes | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">In Geometry, 3D shapes are known as three-dimensional shapes or solids, or solid shapes. 3D shapes or solid shapes have three different measures such as length, width, and height as its dimensions. A polygon is a 2D shape with straight sides. A regular shape has all sides the same length and all int</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/faces-edges-and-vertices/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Faces, Edges And Vertices of 3D Shapes </div> <div class="gfg-similar-read-item-subheading">Faces, Edges, And Vertices of 3D Shapes: Faces, Edges, and Vertices are the three key components that are used to define various 3D objects. They have different dimensions like length, width, and height. In geometry, Faces are the flat surfaces of a 3D shape. They are bounded by edges and are what g</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 11: Mensuration<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/mensuration/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Mensuration in Maths | Formulas for 2D and 3D Shapes, Examples </div> <div class="gfg-similar-read-item-subheading">Mensuration is a branch of mathematics concerned with the calculation of geometric figures and their parameters such as weight, volume, form, surface area, lateral surface area, and so on. Let's learn about all the mensuration formulas in maths. Mensuration MeaningMensuration is the branch of mathem</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">6 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/square/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Square in Maths - Area, Perimeter, Examples & Applications </div> <div class="gfg-similar-read-item-subheading">Square is a type of quadrilateral with four sides. What distinguishes a square from other quadrilaterals is that all four sides of a square are of equal length, and all four interior angles are right angles (90 degrees). Let's learn about Square, including its properties, area, perimeter, examples,</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/triangles/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Triangles in Geometry </div> <div class="gfg-similar-read-item-subheading">Triangles in Geometry: A Triangle is a polygon with three sides and three corners. The corners are also known as vertices, and the sides that connect them are called edges. The interior of a triangle is a two-dimensional region. A triangle is the simplest form of a Polygon. Triangles can be classifi</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">15+ min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/parallelogram/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction to Parallelogram | Properties, Types, and Theorem </div> <div class="gfg-similar-read-item-subheading">A parallelogram is a two-dimensional geometrical shape whose opposite sides are equal in length and parallel. The opposite angles of a parallelogram are equal in measure and the Sum of adjacent angles of a parallelogram is equal to 180 degrees. In this article, we will learn about the definition of</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">12 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/area-of-trapezium-mensuration-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Area of Trapezoid Formula </div> <div class="gfg-similar-read-item-subheading">Area of a trapezoid is a concept in geometry that helps to calculate the space enclosed by the unique quadrilateral. Basically it is measured in square units. In this article we will discuss in detail how to find the area of a trapezoid. Before going to the formula of the area of the trapezoid let's</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/area-of-quadrilateral/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Area of Quadrilateral </div> <div class="gfg-similar-read-item-subheading">Area of Quadrilateral: The Area of a quadrilateral is the space inside the boundary of a quadrilateral or in other words, the space enclosed by the edges of a quadrilateral. A quadrilateral is a closed two-dimensional shape with four sides or edges, and also four corners or vertices. In mensuration,</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/area-of-rhombus/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Area of Rhombus: Formula, Derivation and Examples </div> <div class="gfg-similar-read-item-subheading">Rhombus is a parallelogram in which all four sides are equal and opposite pairs of lines are congruent. The opposite angles in a rhombus are equal. The area of Rhombus is the total space occupied by a Rhombus in a 2d Plane. It is a special type of parallelogram in which all sides are equal to each o</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/area-of-polygons/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Area of Polygons </div> <div class="gfg-similar-read-item-subheading">Area of the Polygon is the area enclosed by the boundary of the polygon. A polygon is a closed, two-dimensional shape with straight sides. Each side of a polygon is a line segment, and the points where the sides meet are called vertices. A polygon is a figure formed by joining 'n' straight lines suc</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">15 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/surface-area-of-cube-cuboid-and-cylinder-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Surface Area of Cube, Cuboid and Cylinder | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">In our daily life, we see many objects like books, pencil boxes, cones, football, cylinder. These all are three-dimensional objects (solid shapes). All these objects occupy some shape and have three dimensions Length, Breadth, Height, or Depth. We often find some shapes with two or more identical (c</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/mensuration-volume-of-cube-cuboid-and-cylinder-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Mensuration - Volume of Cube, Cuboid, and Cylinder | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">Mensuration is the branch of mathematics which deals with the study of different geometrical shapes, their areas, and volume. It uses geometric calculations and algebraic equations to compute the measurement of various aspects of objects like Surface Area, Volume, etc. Volume is the measurement of</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">4 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/volume-and-capacity-mensuration-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Volume and Capacity - Mensuration | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">Mensuration is the branch of mathematics that talks about the length, volume, and area of different geometrical objects. The shape may be in 2-D or 3-D. We find the volume of 3-D objects and the area of 2-D objects. Table of Content What is Volume?What is Capacity?Mensuration of Some Enclosed Figure</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 12: Exponents and Powers<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/laws-of-exponents-use-of-exponents-to-express-small-numbers-in-standard-form-exponents-and-powers-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Laws of Exponents: Exponents and Powers | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">It is known that numbers can be expressed as xn where 'x' is called "Base" and 'n' is called as "Exponent". In simple words, we can say that the Significance of the exponent is that it tells the number of times we need to multiply our base. There are certain Laws of exponents which will make the cal</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">8 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/negative-exponents/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Negative Exponents </div> <div class="gfg-similar-read-item-subheading">Negative Exponents are the exponents with negative values. In other words, negative exponents are the reciprocal of the exponent with similar positive values, i.e. a-n (a negative exponent) can be understood as the reciprocal exponent as 1/an. For example, find the value of (1/2)-2 we can write this</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 14: Factorisation<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/factorization/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Factorization of Polynomial </div> <div class="gfg-similar-read-item-subheading">Factorization is the process in which we can find factors of either a given number or the algebraic expression using various techniques such as prime factorization, factorization using algebraic identities, and factorization of a quadratic polynomial using the middle term splitting method. Factoriza</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">12 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/division-of-algebraic-expressions/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Division of Algebraic Expressions </div> <div class="gfg-similar-read-item-subheading">Division of algebraic expressions is a key operation in algebra. It is essential for simplifying expressions and solving equations. It is used to perform polynomial long division or synthetic division. Division of algebraic expressions is performed as as division on two whole numbers or fractions. I</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">6 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 15: Introduction to Graphs <span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/introduction-to-graphs-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction to Graphs | Class 8 Maths </div> <div class="gfg-similar-read-item-subheading">Graphs are an essential part of mathematics that help visually represent data, making it easier to understand and interpret. In Class 8 Maths, the chapter "Introduction to Graphs" introduces students to the basic concepts and types of graphs. A graph is essentially a visual tool that helps in unders</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">6 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/pie-charts/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Pie Chart </div> <div class="gfg-similar-read-item-subheading">Pie chart is a popular and visually intuitive tool used in data representation, making complex information easier to understand at a glance. This circular graph divides data into slices, each representing a proportion of the whole, allowing for a clear comparison of different categories making it ea</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">13 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/linear-graphs/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">What is Linear Graph? Definition, Equation, Examples </div> <div class="gfg-similar-read-item-subheading">Linear Graph: A Linear Graph is a graphical representation that discusses the relationship between two or more quantities or variables. In the case of any two variables, the relation between these two variables can be drawn by constructing the table of values if the rule for that relation is mention</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/cartesian-plane/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Cartesian Plane </div> <div class="gfg-similar-read-item-subheading">Cartesian plane is defined as the two-dimensional plane used in the Cartesian coordinate system. This plane is formed by intersecting two perpendicular lines called the x-axis and the y-axis and their intersection is called the origin. This method of distributing the 2-Dimensional space into four ar</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Chapter 16: Playing with Numbers<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/playing-with-numbers-class-8-maths/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Playing with Numbers </div> <div class="gfg-similar-read-item-subheading">Playing with Numbers: Numbers are the mathematical objects used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called n</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/letters-for-digits/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Letters for Digits </div> <div class="gfg-similar-read-item-subheading">A number multiplied by 2 gives 60. What is that number? The number is 30. 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