{"id":55166,"date":"2025-01-14T09:58:00","date_gmt":"2025-01-14T04:28:00","guid":{"rendered":"https:\/\/therightmentor.com\/?post_type=chapter&#038;p=55166"},"modified":"2025-01-22T07:45:11","modified_gmt":"2025-01-22T02:15:11","slug":"algebraic-expressions-and-identities-study","status":"publish","type":"chapter","link":"https:\/\/therightmentor.com\/t\/h\/t\/home\/courses\/premium-courses\/premium-courses-regular\/cbse\/cbse-8-mathematics\/cbse-8-mathematics-study\/algebraic-expressions-and-identities-study\/","title":{"rendered":"Algebraic Expressions and Identities | Study"},"content":{"rendered":"\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"padding-right:0;padding-left:0\">\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"padding-right:0;padding-left:0\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\"><div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Mind Map Overal Idea Content Speed Notes Quick Coverage Expressions are formed from variables and constants. Constant: A symbol having a fixed numerical value. Example: 2,, 2.1, etc. (Scroll down till end of the page) Study Tools Audio, Visual &amp; Digital Content Variable: A symbol which takes various numerical values. Example: x, y, z, etc. <a class=\"wp-block-post-excerpt__more-link\" href=\"https:\/\/therightmentor.com\/t\/h\/t\/home\/courses\/premium-courses\/premium-courses-regular\/cbse\/cbse-8-mathematics\/cbse-8-mathematics-study\/algebraic-expressions-and-identities-study\/\">readmore<\/a><\/p><\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"Algebraic expression and identities\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/0CxoaHGb8lU?list=PLEuUy4TjqFeAD5Xcp85qBGE8VHxrYIu7F\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"margin-top:0;margin-bottom:0;padding-right:0;padding-left:0\">\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"padding-top:var(--wp--preset--spacing--20);padding-right:0;padding-bottom:var(--wp--preset--spacing--20);padding-left:0\">\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Click For Contents <\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/therightmentor.com\/t\/h\/t\/home\/courses\/premium-courses\/premium-courses-regular\/cbse\/cbse-8-mathematics\/cbse-8-mathematics-study\/algebraic-expressions-and-identities-study\/#Mind_Map\" >Mind Map<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/therightmentor.com\/t\/h\/t\/home\/courses\/premium-courses\/premium-courses-regular\/cbse\/cbse-8-mathematics\/cbse-8-mathematics-study\/algebraic-expressions-and-identities-study\/#Speed_Notes\" >Speed Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/therightmentor.com\/t\/h\/t\/home\/courses\/premium-courses\/premium-courses-regular\/cbse\/cbse-8-mathematics\/cbse-8-mathematics-study\/algebraic-expressions-and-identities-study\/#Study_Tools\" >Study Tools<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/therightmentor.com\/t\/h\/t\/home\/courses\/premium-courses\/premium-courses-regular\/cbse\/cbse-8-mathematics\/cbse-8-mathematics-study\/algebraic-expressions-and-identities-study\/#Key_Terms\" >Key Terms<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/therightmentor.com\/t\/h\/t\/home\/courses\/premium-courses\/premium-courses-regular\/cbse\/cbse-8-mathematics\/cbse-8-mathematics-study\/algebraic-expressions-and-identities-study\/#Important_Tables\" >Important Tables<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/therightmentor.com\/t\/h\/t\/home\/courses\/premium-courses\/premium-courses-regular\/cbse\/cbse-8-mathematics\/cbse-8-mathematics-study\/algebraic-expressions-and-identities-study\/#Assessments\" >Assessments<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"patron\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Mind_Map\"><\/span>Mind Map<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Overal Idea<\/p>\n\n\n\n<div style=\"height:45px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Content<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"margin-top:var(--wp--preset--spacing--20);margin-bottom:var(--wp--preset--spacing--20);padding-right:0;padding-left:0\">\n<h2 class=\"wp-block-heading\" id=\"patron\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Speed_Notes\"><\/span>Speed Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Quick Coverage<\/p>\n\n\n\n<div style=\"height:45px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Expressions are formed from <strong>variables <\/strong>and <strong>constants.<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Constant: <\/strong>A symbol having a fixed numerical value. <\/p>\n\n\n\n<p>Example: 2,, 2.1, etc. <strong>(Scroll down till end of the page)<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"margin-top:var(--wp--preset--spacing--30);margin-bottom:var(--wp--preset--spacing--30);padding-top:0;padding-right:0;padding-bottom:0;padding-left:0\">\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"padding-right:0;padding-left:0\">\n<h2 class=\"wp-block-heading\" id=\"patron\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Study_Tools\"><\/span>Study Tools<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Audio, Visual &amp; Digital Content<\/p>\n\n\n\n<div style=\"height:45px\" aria-hidden=\"true\" 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Example: x, y, z, etc.<\/p>\n\n\n\n<p><strong>Algebric Expression: <\/strong>A combination of constants and variables connected by the sign<\/p>\n\n\n\n<p>+, -, and is called <strong>algebraic expression<\/strong>.<\/p>\n\n\n\n<p>Terms are added to form <strong>expressions<\/strong>. <\/p>\n\n\n\n<p>Terms themselves are formed as product of factors.<\/p>\n\n\n\n<p>Expressions that contain exactly one, two and three terms are called <strong>monomials<\/strong>, <strong>binomials<\/strong> and <strong>trinomials <\/strong>respectively. <\/p>\n\n\n\n<p>In general, any expression containing one or more terms with non-zero coefficients (and with variables having non- negative exponents) is called a <strong>polynomial<\/strong>.<\/p>\n\n\n\n<p><strong>Like <\/strong>terms are formed from the same variables and the powers of these variables are the same, too. <\/p>\n\n\n\n<p>Coefficients of like terms need not be the same.<\/p>\n\n\n\n<p>While adding (or subtracting) polynomials, first look for like terms and add (or subtract) them; then handle the unlike terms.<\/p>\n\n\n\n<p>There are number of situations in which we need to multiply algebraic expressions: for example, in finding area of a rectangle, the sides of which are given as expressions.<\/p>\n\n\n\n<p><strong>Monomial: <\/strong>An expression containing only one term. Example: -3, 4x, 3xy, etc.<\/p>\n\n\n\n<p><strong>Binomial: <\/strong>An expression containing two terms. Example: 2x-3, 4x+3y, xy-4, etc.,<\/p>\n\n\n\n<p><strong>Polynomial: <\/strong>In general, any expression containing one or more terms with non-zero coefficients (and with variables having non-negative exponents). <\/p>\n\n\n\n<p>A polynomial may contain any number of terms, one or more than one.<\/p>\n\n\n\n<p>A monomial multiplied by a monomial always gives a monomial.<\/p>\n\n\n\n<p><strong>Multiplication of  a Polynomial and a monomial<\/strong>:<\/p>\n\n\n\n<p>While multiplying a polynomial by a monomial, we multiply every term in the <strong>polynomial by the mononomial<\/strong>.<\/p>\n\n\n\n<p><strong><strong>Trinomial<\/strong>: <\/strong>An expression containing three terms. <\/p>\n\n\n\n<p>Example:<\/p>\n\n\n\n<p>3x+2y+5z, etc. <\/p>\n\n\n\n<p>In carrying out the multiplication of a polynomial by a binomial (or trinomial), we multiply term by term, i.e., every term of the polynomial is multiplied by every term in the binomial (or trinomial). <\/p>\n\n\n\n<p><strong>Note<\/strong> that in such multiplication, we may get terms in the product which are like and have to be combined.<\/p>\n\n\n\n<p>An <strong>identity <\/strong>is an equality, which is true for all values of the variables in the equality. <\/p>\n\n\n\n<p>On the other hand, an equation is true only for certain values of its variables. <\/p>\n\n\n\n<p>An equation is not an identity.<\/p>\n\n\n\n<p>The following are the standard identities:<\/p>\n\n\n\n<p>(a + b)<sup>2 <\/sup>= a<sup>2 <\/sup>+ 2ab + b<sup>2<\/sup><\/p>\n\n\n\n<p>(a \u2013 b)<sup>2 <\/sup>= a<sup>2 <\/sup>\u2013 2ab +b<sup>2&nbsp;<\/sup><\/p>\n\n\n\n<p>(a + b)(a \u2013 b) = a<sup>2 <\/sup>\u2013&nbsp; b<sup>2<\/sup><\/p>\n\n\n\n<p>(x + a) (x + b) = x<sup>2<\/sup> + (a + b) x + ab <\/p>\n\n\n\n<p>The above four identities are useful in carrying out squares and products of algebraic expressions. <\/p>\n\n\n\n<p>They also allow easy alternative methods to calculate products of numbers and so on.<\/p>\n\n\n\n<p><strong>Coefficients<\/strong>: In the term of an expression any of the factors with the sign of the term is called the coefficient of the product of the other factors.<\/p>\n\n\n\n<p><strong>Terms<\/strong>: Various parts of an algebraic expression which are separated by + and \u2013 signs. Example: The expression 4x + 5 has two terms 4x and 5.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Constant Term<\/strong>: A term of expression having no lateral factor.<\/li>\n\n\n\n<li><strong>Like term<\/strong>: The term having the same literal factors. Example 2xy and -4xy are like terms.<\/li>\n<\/ol>\n\n\n\n<p>(iii) <strong>Unlike term<\/strong>: The terms having different literal factors. <\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>are unlike terms.<\/p>\n\n\n\n<p>and 3xy<\/p>\n\n\n\n<p><strong>Factors: <\/strong>Each term in an algebraic expression is a product of one or more number (s) and\/or literals. These number (s) and\/or literal (s) are known as the factor of that term. A constant factor is called numerical factor, while a variable factor is known as<\/p>\n\n\n\n<p>a literal factor. The term 4x is the product of its factors 4 and x.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-uagb-container uagb-block-fe53acc0 alignfull uagb-is-root-container\"><div class=\"uagb-container-inner-blocks-wrap\">\n<div class=\"wp-block-uagb-container uagb-block-f7936561\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"Algebraic expression and identities\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/RF3RzIcoJl0?list=PLEuUy4TjqFeBu0qXB7Y1jF7ndP8mup3Kw\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">Hindi Version<\/figcaption><\/figure>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"padding-right:0;padding-left:0\">\n<h2 class=\"wp-block-heading\" id=\"patron\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Key_Terms\"><\/span>Key Terms<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Topic Terminology<\/p>\n\n\n\n<div style=\"height:45px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Term<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-flow wp-block-group-is-layout-flow\" style=\"padding-right:0;padding-left:0\">\n<h2 class=\"wp-block-heading\" id=\"patron\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Important_Tables\"><\/span>Important Tables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>Table:<\/strong><\/p>\n\n\n\n<div style=\"height:45px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>.<\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-text-color has-background has-link-color wp-elements-5193676962d295eb9af99f2157073f0c is-layout-flow wp-block-column-is-layout-flow\" style=\"color:#000000;background-color:#0000000d;padding-top:2em;padding-right:2em;padding-bottom:2em;padding-left:2em\">\n<h2 class=\"wp-block-heading\" id=\"patron\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Assessments\"><\/span>Assessments<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Test Your Learning<\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide is-style-wide--1\"\/>\n\n\n\n\n<div class='ays-quiz-render-callback-box'><\/div>\n\n\n<div class=\"wp-block-buttons has-custom-font-size has-medium-font-size 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https:\/\/therightmentor.com\/wp-content\/uploads\/2024\/04\/TRM-Courses-Thumbnail-1-1-300x300.png 300w, https:\/\/therightmentor.com\/wp-content\/uploads\/2024\/04\/TRM-Courses-Thumbnail-1-1-100x100.png 100w, https:\/\/therightmentor.com\/wp-content\/uploads\/2024\/04\/TRM-Courses-Thumbnail-1-1-600x600.png 600w, https:\/\/therightmentor.com\/wp-content\/uploads\/2024\/04\/TRM-Courses-Thumbnail-1-1-150x150.png 150w, https:\/\/therightmentor.com\/wp-content\/uploads\/2024\/04\/TRM-Courses-Thumbnail-1-1-768x768.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Advanced Tools For Study Assess Interact<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> 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