{"id":73306,"date":"2021-02-05T00:25:33","date_gmt":"2021-02-04T18:55:33","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=73306"},"modified":"2021-02-05T00:25:37","modified_gmt":"2021-02-04T18:55:37","slug":"rd-sharma-chapter-4-class-9-maths-exercise-4-4-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-4-class-9-maths-exercise-4-4-solutions\/","title":{"rendered":"RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions"},"content":{"rendered":"\n<p>RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions is about the sum and difference of cubes. The algebraic expressions will be used but in the cubical form. With the help of this article, students will learn about how to simplify products of the algebraic expressions, that is, to find out the sums and differences of cubes based on the given problems.<\/p>\n<p>We have attached the RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions PDF in which several types of questions will be there with the stepwise solutions given by our experts. The explanations of each problem are given in very easy to understand, and the shortcuts of every problem are also provided with the solutions.<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-4-algebraic-identities\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Learn about RD Sharma Class 9 Chapter 4- Algebraic Identities<\/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-69dbc4a31a049\" 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-69dbc4a31a049\"><\/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-4-class-9-maths-exercise-4-4-solutions\/#download-rd-sharma-chapter-4-class-9-maths-exercise-44-solutions-pdf\" title=\"Download RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions PDF\">Download RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 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-4-class-9-maths-exercise-4-4-solutions\/#important-definitions-rd-sharma-chapter-4-class-9-maths-exercise-44-solutions\" title=\"Important Definitions RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions\">Important Definitions RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-4-class-9-maths-exercise-4-4-solutions\/#frequently-asked-questions-faqs-of-rd-sharma-chapter-4-class-9-maths-exercise-44-solutions\" title=\"Frequently Asked Questions (FAQs) of RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions\">Frequently Asked Questions (FAQs) of RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-4-class-9-maths-exercise-44-solutions-pdf\"><\/span>Download RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 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\/Solutions-for-Class-9-Maths-Chapter-4-Algebraic-Identities-Exercise-4.4.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/Solutions-for-Class-9-Maths-Chapter-4-Algebraic-Identities-Exercise-4.4.pdf\">Solutions for Class 9 Maths Chapter 4 Algebraic Identities Exercise 4.4<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-4-class-9-maths-exercise-44-solutions\"><\/span>Important Definitions RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Here the question comes- \u201cWhat is the Sums and Differences of Cubes? So, the answer is-<\/p>\n<ol>\n<li>A polynomial in form x<sup>3<\/sup> + y<sup>3<\/sup> is called a sum of cubes.<\/li>\n<li>A polynomial in form x<sup>3<\/sup> \u2013 y<sup>3<\/sup> is called a difference of cubes.<\/li>\n<\/ol>\n<p>The questions of this exercise will be solved based on the formulas- Sum and Differences of Cubes mentioned in the following points-<\/p>\n<ul>\n<li>x<sup>3<\/sup> + y<sup>3<\/sup> = (x + y)<sup>3<\/sup> \u2013 3xy (x + y)<\/li>\n<\/ul>\n<p><strong>or<\/strong> x<sup>3<\/sup> + y<sup>3<\/sup> = (x + y) (x<sup>2<\/sup> \u2013 xy + y<sup>2<\/sup>)<\/p>\n<ul>\n<li>x<sup>3<\/sup> \u2013 y<sup>3<\/sup> = (x \u2013 y)<sup>3<\/sup> \u2013 3xy (x \u2013 y)<\/li>\n<\/ul>\n<p><strong>or<\/strong> x<sup>3<\/sup> \u2013 y<sup>3<\/sup> = (x \u2013 y) (x<sup>2<\/sup> + xy + y<sup>2<\/sup>)<\/p>\n<p>Go down to check some examples of the Sums and Differences of Cubes with algebraic expressions-<\/p>\n<p><strong>Ques 1- If p + q = 8 and pq = 6, find the value of p<sup>3<\/sup> + q<sup>3<\/sup>.<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>p+q = 8, pq = 6<\/p>\n<p>Cubing, p+q = 8, both sides, we get<\/p>\n<p>(p + q)<sup>3<\/sup> = (8)<sup>3<\/sup><\/p>\n<p>p<sup>3<\/sup> + q<sup>3<\/sup> + 3pq (p + q) = 512<\/p>\n<p>p<sup>3<\/sup> + q<sup>3<\/sup> + 3 x 6 x 8 = 512<\/p>\n<p>p<sup>3<\/sup> + q<sup>3<\/sup> + 144 = 512<\/p>\n<p>p<sup>3<\/sup> + q<sup>3<\/sup> = 512 \u2013 144 = 368<\/p>\n<p>p<sup>3<\/sup> + q<sup>3<\/sup> = 368<\/p>\n<p><strong>Ques 2- If x + y = 8 and xy = 6, find the value of x<sup>3<\/sup> + y<sup>3<\/sup>.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>x + y = 8, xy = 6<\/p>\n<p>Cubing both sides,<\/p>\n<p>(x + y)<sup>3<\/sup> = (8)<sup>3<\/sup><\/p>\n<p>= x<sup>3<\/sup> + y<sup>3<\/sup> + 3xy (x + y) = 512<\/p>\n<p>= x<sup>3<\/sup> + y<sup>3<\/sup> + 3 x 6 x 8 = 512<\/p>\n<p>= x<sup>3<\/sup> + y<sup>3<\/sup> + 144 = 512<\/p>\n<p>= x<sup>3<\/sup> + y<sup>3<\/sup> = 512 \u2013 144 = 368<\/p>\n<p>Therefore, x<sup>3<\/sup> + y<sup>3<\/sup> = 368<\/p>\n<p><strong>Ques 3- If a \u2013 b = 6 and ab = 20, find the value of a<sup>3<\/sup>&#8211; b<sup>3<\/sup>.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>p \u2013 q = 6, pq = 20<\/p>\n<p>Cubing both sides,<\/p>\n<p>(p \u2013 q)3 = (6)<sup>3<\/sup><\/p>\n<p>= p<sup>3<\/sup> \u2013 q<sup>3<\/sup> \u2013 3pq (p \u2013 q) = 216<\/p>\n<p>= p<sup>3<\/sup> \u2013 q<sup>3<\/sup> \u2013 3 x 20 x 6 = 216<\/p>\n<p>= p<sup>3<\/sup> \u2013 q<sup>3<\/sup> \u2013 360 = 216<\/p>\n<p>= p<sup>3<\/sup> \u2013 q<sup>3<\/sup> = 216 + 360 = 576<\/p>\n<p>Therefore, p<sup>3<\/sup> \u2013 q<sup>3<\/sup> = 576<\/p>\n<h2><span class=\"ez-toc-section\" id=\"frequently-asked-questions-faqs-of-rd-sharma-chapter-4-class-9-maths-exercise-44-solutions\"><\/span>Frequently Asked Questions (FAQs) of RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Ques 1- How do you find the sum of a cube?<\/strong><\/p>\n<p><strong>Ans-<\/strong> It shows that the sum is constantly square, but what is even more exceptional is that the sum of the first n cubes, 13+23+&#8230; + n 3 = (n (n +1)\/2)2, which is the square of the nth triangle number.<\/p>\n<p>For Example-<\/p>\n<p>13+23+&#8230;+103 = (10\u00d711\/2)2 = 552 = 3025.<\/p>\n<p><strong>Ques 2- How do you factor the sum and difference of two cubes?<\/strong><\/p>\n<p><strong>Ans-<\/strong> The sum or difference of two cubes will be factored into a product of binomial times a trinomial.<\/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 4 Class 9 Maths Exercise 4.4 Solutions is about the sum and difference of cubes. The algebraic expressions will be used but in the cubical form. With the help of this article, students will learn about how to simplify products of the algebraic expressions, that is, to find out the sums and &#8230; <a title=\"RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-4-class-9-maths-exercise-4-4-solutions\/\" aria-label=\"More on RD Sharma Chapter 4 Class 9 Maths Exercise 4.4 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":73308,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2917,73719,73411,2985],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73306"}],"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=73306"}],"version-history":[{"count":3,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73306\/revisions"}],"predecessor-version":[{"id":73596,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/73306\/revisions\/73596"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/73308"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=73306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=73306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=73306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}