{"id":125271,"date":"2023-09-03T13:09:00","date_gmt":"2023-09-03T07:39:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=125271"},"modified":"2023-10-31T10:15:47","modified_gmt":"2023-10-31T04:45:47","slug":"rd-sharma-class-9-solutions-chapter-5-exercise-5-1","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-5-exercise-5-1\/","title":{"rendered":"RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1 (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-125865\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-5-Exercise-5.1.jpg\" alt=\"RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-5-Exercise-5.1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-5-Exercise-5.1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1: <\/strong>You can download the Free PDF of <span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4540,&quot;5&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;6&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;7&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;8&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;10&quot;:2,&quot;11&quot;:0,&quot;15&quot;:&quot;Arial&quot;}\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-5-factorization-of-algebraic-expressions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Class 9 Solutions Chapter 5 <\/a> Exercise 5.1 using the link mentioned in our blog. You can easily learn the concepts of Class 9 Maths with this amazing guide. All your Maths assignments and tests will be covered in this. To know more about the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-for-maths\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 9 Maths<\/a>, read the whole blog.<\/span><\/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-69e753443ffc9\" 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 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ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-5-exercise-5-1\/#faqs-on-rd-sharma-class-9-solutions-for-chapter-5-exercise-51\" title=\"FAQs on RD Sharma Class 9 Solutions for Chapter 5 Exercise 5.1\">FAQs on RD Sharma Class 9 Solutions for Chapter 5 Exercise 5.1<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-5-exercise-5-1\/#how-many-questions-are-there-in-rd-sharma-class-9-solutions-chapter-5-exercise-51\" title=\"How many questions are there in RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1?\">How many questions are there in RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-5-exercise-5-1\/#from-where-can-i-download-the-pdf-of-rd-sharma-solutions-class-9-maths-chapter-5-exercise-51\" title=\"From where can I download the PDF of RD Sharma Solutions Class 9 Maths Chapter 5 Exercise 5.1?\">From where can I download the PDF of RD Sharma Solutions Class 9 Maths Chapter 5 Exercise 5.1?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-5-exercise-5-1\/#how-much-does-it-cost-to-download-the-pdf-of-rd-sharma-solutions-class-9-maths-chapter-5-exercise-51\" title=\"How much does it cost to download the PDF of RD Sharma Solutions Class 9 Maths Chapter 5 Exercise 5.1\">How much does it cost to download the PDF of RD Sharma Solutions Class 9 Maths Chapter 5 Exercise 5.1<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-9-solutions-chapter-5-exercise-51-pdf\"><\/span><strong>Download RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1<span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4540,&quot;5&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;6&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;7&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;8&quot;:{&quot;1&quot;:[{&quot;1&quot;:2,&quot;2&quot;:0,&quot;5&quot;:[null,2,0]},{&quot;1&quot;:0,&quot;2&quot;:0,&quot;3&quot;:3},{&quot;1&quot;:1,&quot;2&quot;:0,&quot;4&quot;:1}]},&quot;10&quot;:2,&quot;11&quot;:0,&quot;15&quot;:&quot;Arial&quot;}\">\u00a0PDF<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-SHARMA-Solutions-Class-9-Maths-Chapter-5-Ex-5.1.pdf\">RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1<\/a><\/p>\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\/09\/RD-SHARMA-Solutions-Class-9-Maths-Chapter-5-Ex-5.1.pdf\", \"#example1\");<\/script><\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-answers-of-rd-sharma-class-9-solutions-chapter-5-exercise-51\"><\/span><strong>Access answers of <\/strong><strong>RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h4><span class=\"ez-toc-section\" id=\"exercise-51-page-no-59\"><\/span>Exercise 5.1 Page No: 5.9<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Question 1: Factorize x<sup>3<\/sup>\u00a0+ x \u2013 3x<sup>2<\/sup>\u00a0\u2013 3<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>x<sup>3<\/sup>\u00a0+ x \u2013 3x<sup>2<\/sup>\u00a0\u2013 3<\/p>\n<p>Here x is common factor in x<sup>3<\/sup>\u00a0+ x and \u2013 3 is common factor in \u2013 3x<sup>2<\/sup>\u00a0\u2013 3<\/p>\n<p>x<sup>3<\/sup>\u00a0\u2013 3x<sup>2<\/sup>\u00a0+ x \u2013 3<\/p>\n<p>x<sup>2<\/sup>\u00a0(x \u2013 3) + 1(x \u2013 3)<\/p>\n<p>Taking ( x \u2013 3) common<\/p>\n<p>(x \u2013 3) (x<sup>2<\/sup>\u00a0+ 1)<\/p>\n<p>Therefore x<sup>3<\/sup>\u00a0+ x \u2013 3x<sup>2<\/sup>\u00a0\u2013 3 = (x \u2013 3) (x<sup>2<\/sup>\u00a0+ 1)<\/p>\n<p><strong>Question 2: Factorize a(a + b)<sup>3<\/sup>\u00a0\u2013 3a<sup>2<\/sup>b(a + b)<\/strong><\/p>\n<p><strong>Solution<\/strong>:<\/p>\n<p>a(a + b)<sup>3<\/sup>\u00a0\u2013 3a<sup>2<\/sup>b(a + b)<\/p>\n<p>Taking a(a + b) as common factor<\/p>\n<p>= a(a + b) {(a + b)<sup>2<\/sup>\u00a0\u2013 3ab}<\/p>\n<p>= a(a + b) {a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>\u00a0+ 2ab \u2013 3ab}<\/p>\n<p>= a(a + b) (a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>\u00a0\u2013 ab)<\/p>\n<p><strong>Question 3: Factorize x(x<sup>3<\/sup>\u00a0\u2013 y<sup>3<\/sup>) + 3xy(x \u2013 y)<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>x(x<strong><sup>3<\/sup><\/strong>\u00a0\u2013 y<strong><sup>3<\/sup><\/strong>) + 3xy(x \u2013 y)<\/p>\n<p>= x(x \u2013 y) (x<sup>2<\/sup>\u00a0+ xy + y<sup>2<\/sup>) + 3xy(x \u2013 y)<\/p>\n<p>Taking x(x \u2013 y) as a common factor<\/p>\n<p>= x(x \u2013 y) (x<sup>2<\/sup>\u00a0+ xy + y<sup>2<\/sup>\u00a0+ 3y)<\/p>\n<p>= x(x \u2013 y) (x<sup>2<\/sup>\u00a0+ xy + y<sup>2<\/sup>\u00a0+ 3y)<\/p>\n<p><strong>Question 4: Factorize a<sup>2<\/sup>x<sup>2<\/sup>\u00a0+ (ax<sup>2<\/sup>\u00a0+ 1)x + a<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>a<sup>2<\/sup>x<sup>2<\/sup>\u00a0+ (ax<sup>2<\/sup>\u00a0+ 1)x + a<\/p>\n<p>= a<sup>2<\/sup>x<sup>2<\/sup>\u00a0+ a + (ax<sup>2<\/sup>\u00a0+ 1)x<\/p>\n<p>= a(ax<sup>2<\/sup>\u00a0+ 1) + x(ax<sup>2<\/sup>\u00a0+ 1)<\/p>\n<p>= (ax<sup>2<\/sup>\u00a0+ 1) (a + x)<\/p>\n<p><strong>Question 5: Factorize x<sup>2<\/sup>\u00a0+ y \u2013 xy \u2013 x<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>x<sup>2<\/sup>\u00a0+ y \u2013 xy \u2013 x<\/p>\n<p>= x<sup>2\u00a0<\/sup>\u2013 x \u2013 xy + y<\/p>\n<p>= x(x- 1) \u2013 y(x \u2013 1)<\/p>\n<p>= (x \u2013 1) (x \u2013 y)<\/p>\n<p><strong>Question 6: Factorize x<sup>3<\/sup>\u00a0\u2013 2x<sup>2<\/sup>y + 3xy<sup>2<\/sup>\u00a0\u2013 6y<sup>3<\/sup><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>x<sup>3<\/sup>\u00a0\u2013 2x<sup>2<\/sup>y + 3xy<sup>2<\/sup>\u00a0\u2013 6y<sup>3<\/sup><\/p>\n<p>= x<sup>2<\/sup>(x \u2013 2y) + 3y<sup>2<\/sup>(x \u2013 2y)<\/p>\n<p>= (x \u2013 2y) (x<sup>2<\/sup>\u00a0+ 3y<sup>2<\/sup>)<\/p>\n<p><strong>Question 7: Factorize 6ab \u2013 b<sup>2<\/sup>\u00a0+ 12ac \u2013 2bc<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>6ab \u2013 b<sup>2<\/sup>\u00a0+ 12ac \u2013 2bc<\/p>\n<p>= 6ab + 12ac \u2013 b<sup>2<\/sup>\u00a0\u2013 2bc<\/p>\n<p>Taking 6a common from the first two terms and \u2013b from the last two terms<\/p>\n<p>= 6a(b + 2c) \u2013 b(b + 2c)<\/p>\n<p>Taking (b + 2c) common factor<\/p>\n<p>= (b + 2c) (6a \u2013 b)<\/p>\n<p><strong>Question 8: Factorize (x<sup>2<\/sup>\u00a0+ 1\/x<sup>2<\/sup>) \u2013 4(x + 1\/x) + 6<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>(x<sup>2<\/sup>\u00a0+ 1\/x<sup>2<\/sup>) \u2013 4(x + 1\/x) + 6<\/p>\n<p>= x<sup>2<\/sup>\u00a0+ 1\/x<sup>2<\/sup>\u00a0\u2013 4x \u2013 4\/x + 4 + 2<\/p>\n<p>= x<sup>2<\/sup>\u00a0+ 1\/x<sup>2<\/sup>\u00a0+ 4 + 2 \u2013 4\/x \u2013 4x<\/p>\n<p>= (x<sup>2<\/sup>) + (1\/x)<sup>\u00a02<\/sup>\u00a0+ (-2)<sup>2<\/sup>\u00a0+ 2x(1\/x) + 2(1\/x)(-2) + 2(-2)x<\/p>\n<p>As we know, x<sup>2<\/sup>\u00a0+ y<sup>2<\/sup>\u00a0+ z<sup>2<\/sup>\u00a0+ 2xy + 2yz + 2zx = (x+y+z)<sup>\u00a02<\/sup><\/p>\n<p>So, we can write;<\/p>\n<p>= (x + 1\/x + (-2 ))<sup>\u00a02<\/sup><\/p>\n<p>or (x + 1\/x \u2013 2)<sup>\u00a02<\/sup><\/p>\n<p>Therefore, x<sup>2<\/sup>\u00a0+ 1\/x<sup>2<\/sup>) \u2013 4(x + 1\/x) + 6 = (x + 1\/x \u2013 2)<sup>\u00a02<\/sup><\/p>\n<p><strong>Question 9: Factorize x(x \u2013 2) (x \u2013 4) + 4x \u2013 8<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>x(x \u2013 2) (x \u2013 4) + 4x \u2013 8<\/p>\n<p>= x(x \u2013 2) (x \u2013 4) + 4(x \u2013 2)<\/p>\n<p>= (x \u2013 2) [x(x \u2013 4) + 4]<\/p>\n<p>= (x \u2013 2) (x<sup>2<\/sup>\u00a0\u2013 4x + 4)<\/p>\n<p>= (x \u2013 2) [x<sup>2<\/sup>\u00a0\u2013 2 (x)(2) + (2)<sup>\u00a02<\/sup>]<\/p>\n<p>= (x \u2013 2) (x \u2013 2)<sup>\u00a02<\/sup><\/p>\n<p>= (x \u2013 2)<sup>3<\/sup><\/p>\n<p><strong>Question 10: Factorize ( x + 2 ) ( x<sup>2<\/sup>\u00a0+ 25 ) \u2013 10x<sup>2<\/sup>\u00a0\u2013 20x<\/strong><\/p>\n<p><strong>Solution :<\/strong><\/p>\n<p>( x + 2) ( x<sup>2<\/sup>\u00a0+ 25) \u2013 10x ( x + 2 )<\/p>\n<p>Take ( x + 2 ) as common factor;<\/p>\n<p>= ( x + 2 )( x<strong><sup>2\u00a0<\/sup><\/strong>+ 25 \u2013 10x)<\/p>\n<p>=( x + 2 ) ( x<strong><sup>2\u00a0<\/sup><\/strong>\u2013 10x + 25)<\/p>\n<p>Expanding the middle term of ( x<sup>2<\/sup>\u00a0\u2013 10x + 25 )<\/p>\n<p>=( x + 2 ) ( x<strong><sup>2\u00a0<\/sup><\/strong>\u2013 5x \u2013 5x + 25 )<\/p>\n<p>=( x + 2 ){ x (x \u2013 5 ) \u2013 5 ( x \u2013 5 )}<\/p>\n<p>=( x + 2 )( x \u2013 5 )( x \u2013 5 )<\/p>\n<p>=( x + 2 )( x \u2013 5 )<sup>2<\/sup><\/p>\n<p>Therefore, ( x + 2) ( x<sup>2<\/sup>\u00a0+ 25) \u2013 10x ( x + 2 ) = ( x + 2 )( x \u2013 5 )<sup>2<\/sup><\/p>\n<p><strong>Question 11: Factorize 2a<sup>2<\/sup>\u00a0+ 2\u221a6 ab + 3b<sup>2<\/sup><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>2a<sup>2<\/sup>\u00a0+ 2\u221a6 ab + 3b<sup>2<\/sup><\/p>\n<p>Above expression can be written as ( \u221a2a )<sup>2<\/sup>\u00a0+ 2 \u00d7 \u221a2a \u00d7 \u221a3b + ( \u221a3b)<sup>2<\/sup><\/p>\n<p>As we know, ( p + q )<sup>\u00a02\u00a0<\/sup>= p<sup>2\u00a0<\/sup>+ q<sup>2<\/sup>\u00a0+ 2pq<\/p>\n<p>Here p = \u221a2a and q = \u221a3b<\/p>\n<p>= (\u221a2a + \u221a3b )<sup>2<\/sup><\/p>\n<p>Therefore, 2a<sup>2<\/sup>\u00a0+ 2\u221a6 ab + 3b<sup>2<\/sup>\u00a0= (\u221a2a + \u221a3b )<sup>2<\/sup><\/p>\n<p><strong>Question 12: Factorize (a \u2013 b + c)<sup>2<\/sup>\u00a0+ (b \u2013 c + a)<sup>\u00a02<\/sup>\u00a0+ 2(a \u2013 b + c) (b \u2013 c + a)<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>(a \u2013 b + c)<sup>2<\/sup>\u00a0+ ( b \u2013 c + a)<sup>\u00a02<\/sup>\u00a0+ 2(a \u2013 b + c) (b \u2013 c + a)<\/p>\n<p>{Because p<sup>2\u00a0<\/sup>+ q<sup>2<\/sup>\u00a0+ 2pq = (p + q)<sup>\u00a02<\/sup>}<\/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]<sup>2<\/sup><\/p>\n<p>= (2a)<sup>2<\/sup><\/p>\n<p>= 4a<sup>2<\/sup><\/p>\n<p><strong>Question 13: Factorize a<sup>2<\/sup>\u00a0+ b<sup>2\u00a0<\/sup>+ 2( ab+bc+ca )<\/strong><\/p>\n<p><strong>Solution<\/strong>:<\/p>\n<p>a<sup>2<\/sup>\u00a0+ b<sup>2\u00a0<\/sup>+ 2ab + 2bc + 2ca<\/p>\n<p>As we know, p<sup>2\u00a0<\/sup>+ q<sup>2<\/sup>\u00a0+ 2pq = (p + q)<sup>\u00a02<\/sup><\/p>\n<p>We get,<\/p>\n<p>= ( a+b)<sup>2<\/sup>\u00a0+ 2bc + 2ca<\/p>\n<p>= ( a+b)<sup>2<\/sup>\u00a0+ 2c( b + a )<\/p>\n<p>Or ( a+b)<sup>2<\/sup>\u00a0+ 2c( a + b )<\/p>\n<p>Take ( a + b ) as a common factor;<\/p>\n<p>= ( a + b )( a + b + 2c )<\/p>\n<p>Therefore, a<sup>2<\/sup>\u00a0+ b<sup>2\u00a0<\/sup>+ 2ab + 2bc + 2ca = ( a + b )( a + b + 2c )<\/p>\n<p><strong>Question 14: Factorize 4(x-y)<sup>\u00a02<\/sup>\u00a0\u2013 12(x \u2013 y)(x + y) + 9(x + y)<sup>2<\/sup><\/strong><\/p>\n<p><strong>Solution :<\/strong><\/p>\n<p>Consider ( x \u2013 y ) = p, ( x + y ) = q<\/p>\n<p>= 4p<sup>2<\/sup>\u00a0\u2013 12pq + 9q<sup>2<\/sup><\/p>\n<p>Expanding the middle term, -12 = -6 -6 also 4\u00d7 9=-6 \u00d7 -6<\/p>\n<p>= 4p<sup>2<\/sup>\u00a0\u2013 6pq \u2013 6pq + 9q<sup>2<\/sup><\/p>\n<p>=2p( 2p \u2013 3q ) -3q( 2p \u2013 3q )<\/p>\n<p>= ( 2p \u2013 3q ) ( 2p \u2013 3q )<\/p>\n<p>= ( 2p \u2013 3q )<sup>2<\/sup><\/p>\n<p>Substituting back p = x \u2013 y and q = x + y;<\/p>\n<p>= [2( x-y ) \u2013 3( x+y)]<sup>2\u00a0<\/sup>= [ 2x \u2013 2y \u2013 3x \u2013 3y ]<sup>\u00a02<\/sup><\/p>\n<p>= (2x-3x-2y-3y )<sup>\u00a02<\/sup><\/p>\n<p>=[ -x \u2013 5y]<sup>\u00a02<\/sup><\/p>\n<p>=[( -1 )( x+5y )]<sup>\u00a02<\/sup><\/p>\n<p>=( x+5y )<sup>\u00a02<\/sup><\/p>\n<p>Therefore, 4(x-y)<sup>\u00a02<\/sup>\u00a0\u2013 12(x \u2013 y)(x + y) + 9(x + y)<sup>2<\/sup>\u00a0= ( x+5y )<sup>2<\/sup><\/p>\n<p><strong>Question 15: Factorize a<sup>2<\/sup>\u00a0\u2013 b<sup>2\u00a0<\/sup>+ 2bc \u2013 c<sup>2<\/sup><\/strong><\/p>\n<p><strong>Solution :<\/strong><\/p>\n<p>a<sup>2<\/sup>\u00a0\u2013 b<sup>2\u00a0<\/sup>+ 2bc \u2013 c<sup>2<\/sup><\/p>\n<p>As we know, ( a-b)<sup>2<\/sup>\u00a0= a<sup>2\u00a0<\/sup>+ b<sup>2\u00a0<\/sup>\u2013 2ab<\/p>\n<p>= a<sup>2\u00a0<\/sup>\u2013 ( b \u2013 c)<sup>\u00a02<\/sup><\/p>\n<p>Also we know, a<sup>2\u00a0<\/sup>\u2013 b<sup>2\u00a0<\/sup>= ( a+b)( a-b)<\/p>\n<p>= ( a + b \u2013 c )( a \u2013 ( b \u2013 c ))<\/p>\n<p>= ( a + b \u2013 c )( a \u2013 b + c )<\/p>\n<p>Therefore, a<sup>2<\/sup>\u00a0\u2013 b<sup>2\u00a0<\/sup>+ 2bc \u2013 c<sup>2\u00a0<\/sup>=( a + b \u2013 c )( a \u2013 b + c )<\/p>\n<p><strong>Question 16: Factorize a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>\u00a0\u2013 c<sup>2<\/sup><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>\u00a0\u2013 c<sup>2<\/sup><\/p>\n<p>= (a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>) \u2013 c<sup>2<\/sup><\/p>\n<p>= (a + b)<sup>2<\/sup>\u00a0\u2013 (c)<sup>\u00a02<\/sup><\/p>\n<p>We know, a<sup>2<\/sup>\u00a0\u2013 b<sup>2<\/sup>\u00a0= (a + b) (a \u2013 b)<\/p>\n<p>= (a + b + c) (a + b \u2013 c)<\/p>\n<p>Therefore a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>\u00a0\u2013 c<sup>2\u00a0<\/sup>= (a + b + c) (a + b \u2013 c)<\/p>\n<hr \/>\n<p>This is the complete blog on RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1. To know more about the <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a> Class 9 Maths exam, ask in the comments.\u00a0<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-9-solutions-for-chapter-5-exercise-51\"><\/span><strong>FAQs on RD Sharma Class 9 Solutions for Chapter 5 Exercise 5.1<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1631085637096\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-there-in-rd-sharma-class-9-solutions-chapter-5-exercise-51\"><\/span>How many questions are there in RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are 36 questions in\u00a0RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631085771652\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"from-where-can-i-download-the-pdf-of-rd-sharma-solutions-class-9-maths-chapter-5-exercise-51\"><\/span>From where can I download the PDF of RD Sharma Solutions Class 9 Maths Chapter 5 Exercise 5.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can find the download link from the above blog.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631085794671\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-much-does-it-cost-to-download-the-pdf-of-rd-sharma-solutions-class-9-maths-chapter-5-exercise-51\"><\/span>How much does it cost to download the PDF of RD Sharma Solutions Class 9 Maths Chapter 5 Exercise 5.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download it for free.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1: You can download the Free PDF of RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1 using the link mentioned in our blog. You can easily learn the concepts of Class 9 Maths with this amazing guide. All your Maths assignments and tests will be covered &#8230; <a title=\"RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1 (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-9-solutions-chapter-5-exercise-5-1\/\" aria-label=\"More on RD Sharma Class 9 Solutions Chapter 5 Exercise 5.1 (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":243,"featured_media":125865,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411],"tags":[3086,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125271"}],"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\/243"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=125271"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125271\/revisions"}],"predecessor-version":[{"id":499596,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125271\/revisions\/499596"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/125865"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=125271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=125271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=125271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}