{"id":73331,"date":"2021-02-05T22:25:31","date_gmt":"2021-02-05T16:55:31","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=73331"},"modified":"2021-02-05T22:25:34","modified_gmt":"2021-02-05T16:55:34","slug":"rd-sharma-chapter-5-class-9-maths-exercise-5-1-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-5-class-9-maths-exercise-5-1-solutions\/","title":{"rendered":"RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions"},"content":{"rendered":"\n<p>RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions is all about the Factorization of the Algebraic Expression. Students will get to know how to solve the various types of Algebraic Expressions like- monomials, binomials, trinomials, and polynomials using identities. Before going to any problems of this chapter, students are suggested to learn the formulas related to it, which helps them solve questions more quickly.<\/p>\n<p>In the following RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions PDF, learners understand the concept of the Factorization of the Algebraic Expressions through the solved problems based on the CBSE and RD Sharma of Class 9. The PDF is prepared by professionals with a complete explanation of each question.<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-5-factorization-of-algebraic-expressions\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Learn about RD Sharma Class 9 Chapter 5- Factorization of the Algebraic Expression<\/strong><\/a><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of 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=\"ez-toc-toggle-icon-1\"><label for=\"item-69fd7cf706a45\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" 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: #000000;color:#000000\" 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><\/label><input  type=\"checkbox\" id=\"item-69fd7cf706a45\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-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:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-5-class-9-maths-exercise-5-1-solutions\/#download-rd-sharma-chapter-5-class-9-maths-exercise-51-solutions-pdf\" title=\"Download RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions PDF\">Download RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-5-class-9-maths-exercise-5-1-solutions\/#important-definitions-rd-sharma-chapter-5-class-9-maths-exercise-51-solutions\" title=\"Important Definitions RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions\">Important Definitions RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-5-class-9-maths-exercise-51-solutions-pdf\"><\/span>Download RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/Class-9-Maths-Chapter-5-Factorization-of-Algebraic-Expressions-Exercise-5.1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/Class-9-Maths-Chapter-5-Factorization-of-Algebraic-Expressions-Exercise-5.1.pdf\">Class 9 Maths Chapter 5 Factorization of Algebraic Expressions Exercise 5.1<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-5-class-9-maths-exercise-51-solutions\"><\/span>Important Definitions RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Go down to check the topics of Factorization of Algebraic Expressions from which simplification of the questions are given in the above PDF-<\/p>\n<ol>\n<li>Factorization by taking out the common factors<\/li>\n<li>Factorization by grouping the terms<\/li>\n<li>Factorization by making a perfect square<\/li>\n<li>Factorization by the difference of two squares<\/li>\n<li>Factorization of quadratic polynomials by splitting the middle term<\/li>\n<\/ol>\n<p>Here are some examples with the solutions of the topics of Factorization of Algebraic Expressions-<\/p>\n<p><strong>Ques-<\/strong> <strong>a<\/strong><strong>2<\/strong><strong> + 2ab + b<\/strong><strong>2<\/strong><strong> \u2013 c<\/strong><strong>2<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>p2 + 2pq + q2 \u2013 r2<\/p>\n<p>= (p2 + 2pq + q2) \u2013 r2<\/p>\n<p>= (p + q)2 \u2013 (r) 2<\/p>\n<p>Algebraic Identitty- p2 \u2013 q2 = (p + q) (p \u2013 q)<\/p>\n<p>= (p + q + r) (p + q \u2013 r)<\/p>\n<p>Therefore p2 + 2pq + q2 \u2013 r2 = (p + q + r) (p + q \u2013 r)<\/p>\n<p><strong>Ques- (a \u2013 b + c)<\/strong><strong>2<\/strong><strong> + (b \u2013 c + a)<\/strong><strong> 2<\/strong><strong> + 2(a \u2013 b + c) (b \u2013 c + a)<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>(a \u2013 b + c)2 + (b \u2013 c + a) 2 + 2 (a \u2013 b + c) (b \u2013 c + a)<\/p>\n<p>{Because p2 + q2 + 2pq = (p + q) 2}<\/p>\n<p>Here p = a \u2013 b + c and q = b \u2013 c + a<\/p>\n<p>= [a \u2013 b + c + b- c + a]2<\/p>\n<p>= (2a)2<\/p>\n<p>= 4a2<\/p>\n<p><strong>Ques- (x<\/strong><strong>2<\/strong><strong> + 1\/x<\/strong><strong>2<\/strong><strong>) \u2013 4(x + 1\/x) + 6<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>(x2 + 1\/x2) \u2013 4(x + 1\/x) + 6<\/p>\n<p>= x2 + 1\/x2 \u2013 4x \u2013 4\/x + 4 + 2<\/p>\n<p>= x2 + 1\/x2 + 4 + 2 \u2013 4\/x \u2013 4x<\/p>\n<p>= (x2) + (1\/x) 2 + (-2)2 + 2x(1\/x) + 2(1\/x)(-2) + 2(-2)x<\/p>\n<p>As we know, x2 + y2 + z2 + 2xy + 2yz + 2zx = (x+y+z) 2<\/p>\n<p>So, we can write;<\/p>\n<p>= (x + 1\/x + (-2 )) 2<\/p>\n<p>or (x + 1\/x \u2013 2) 2<\/p>\n<p>Therefore, (x2 + 1\/x2) \u2013 4(x + 1\/x) + 6 = (x + 1\/x \u2013 2) 2<\/p>\n<p><strong>Ques- 2a<\/strong><strong>2<\/strong><strong> + 2\u221a6 ab + 3b<\/strong><strong>2<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>2a2 + 2\u221a6 ab + 3b2<\/p>\n<p>Above expression can be written as ( \u221a2a )2 + 2 \u00d7 \u221a2a \u00d7 \u221a3b + ( \u221a3b)2<\/p>\n<p>As we know, ( p + q ) 2 = p2 + q2 + 2pq<\/p>\n<p>Here p = \u221a2a and q = \u221a3b<\/p>\n<p>= (\u221a2a + \u221a3b )2<\/p>\n<p>Therefore, 2a2 + 2\u221a6 ab + 3b2 = (\u221a2a + \u221a3b )2<\/p>\n<p><a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Know about CBSE Board<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions is all about the Factorization of the Algebraic Expression. Students will get to know how to solve the various types of Algebraic Expressions like- monomials, binomials, trinomials, and polynomials using identities. Before going to any problems of this chapter, students are suggested to learn the &#8230; <a title=\"RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-5-class-9-maths-exercise-5-1-solutions\/\" aria-label=\"More on RD Sharma Chapter 5 Class 9 Maths Exercise 5.1 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":73333,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73719,73411,73410],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73331"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/241"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=73331"}],"version-history":[{"count":2,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73331\/revisions"}],"predecessor-version":[{"id":73793,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73331\/revisions\/73793"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/73333"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=73331"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=73331"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=73331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}