{"id":71976,"date":"2021-01-28T16:06:41","date_gmt":"2021-01-28T10:36:41","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=71976"},"modified":"2023-12-20T10:29:20","modified_gmt":"2023-12-20T04:59:20","slug":"rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions\/","title":{"rendered":"RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions 2024"},"content":{"rendered":"\n<p>RS Aggarwal Chapter 3 Class 9 Maths Exercise 3.1 Solutions: Some more algebraic identities are discussed in this chapter. It can be used in the factoring and calculation of some given expressions. Also, this chapter discusses various polynomials based on the number of words. RS Aggarwal Solution for Class 9 Mathematics Solutions Chapter 3 by KopyKitab sets a benchmark for you that perfectly prepares and resolves any type of test question regardless of difficulty. Level.<\/p>\n<p>The third section of RS Aggarwal Solutions for Class 9, Chapter 3, contains essentially 34 questions that rely on factoring techniques and methods to collect polynomials using factoring. There are many questions about factoring and factoring methods by grouping.<\/p>\n<p>Other exercises <a href=\"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-solutions-class-9-maths-chapter-3-factorisation-of-polynomials\/\">here<\/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-69d008c1a94bd\" 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-69d008c1a94bd\"><\/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\/rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions\/#download-rs-aggarwal-chapter-3-class-9-maths-exercise-31-solutions\" title=\"Download RS Aggarwal Chapter 3 Class 9 Maths Exercise 3.1 Solutions\">Download RS Aggarwal Chapter 3 Class 9 Maths Exercise 3.1 Solutions<\/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\/rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions\/#important-definition-for-rs-aggarwal-chapter-3-class-9-maths-exercise-31-solutions\" title=\"Important Definition for RS Aggarwal Chapter 3 Class 9 Maths Exercise 3.1 Solutions\">Important Definition for RS Aggarwal Chapter 3 Class 9 Maths Exercise 3.1 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\/rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions\/#faqs-on-rs-aggarwal-chapter-3-class-9-maths-exercises-31-ex-3a-solutions\" title=\"FAQs on RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions\">FAQs on RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions\/#from-where-can-i-download-the-pdf-of-rs-aggarwal-chapter-3-class-9-maths-exercises-31-ex-3a-solutions\" title=\"From where can I download the PDF of RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions?\">From where can I download the PDF of RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions\/#how-much-does-it-cost-to-download-the-pdf-of-rs-aggarwal-chapter-3-class-9-maths-exercises-31-ex-3a-solutions\" title=\"How much does it cost to download the PDF of RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions?\">How much does it cost to download the PDF of RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions?<\/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\/rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions\/#can-i-access-the-rs-aggarwal-chapter-3-class-9-maths-exercises-31-ex-3a-solutions-pdf-offline\" title=\"Can I access the RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions PDF offline?\">Can I access the RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions PDF offline?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rs-aggarwal-chapter-3-class-9-maths-exercise-31-solutions\"><\/span>Download RS Aggarwal Chapter 3 Class 9 Maths Exercise 3.1 Solutions<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\/01\/EXERCISE-\u2013-3A.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/EXERCISE-\u2013-3A.pdf\">EXERCISE \u2013 3A<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definition-for-rs-aggarwal-chapter-3-class-9-maths-exercise-31-solutions\"><\/span>Important Definition for RS Aggarwal Chapter 3 Class 9 Maths Exercise 3.1 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong><b>Factorization:<\/b><\/strong> To precise a given polynomial as the item of polynomials each of degree less than that of the given polynomial such that no such a factor contains a calculated lower degree, is called factorization.<\/p>\n<p><strong><b>A polynomial<\/b><\/strong> can be\u00a0spoken to\u00a0as an\u00a0item\u00a0of polynomials with its degree less than or\u00a0equal.\u00a0Each\u00a0polynomial that is included to\u00a0discover\u00a0the\u00a0product\u00a0is called a factor. A polynomial can be\u00a0spoken to\u00a0as an\u00a0item\u00a0of polynomials with its degree less than or\u00a0rise to\u00a0it.<\/p>\n<p>Each polynomial that is included to discover the product is called calculates. The process included in breaking a polynomial and making it as a product of its figure is called the Factorisation of Polynomials.<\/p>\n<p><strong><b>Constants<\/b><\/strong>: Fixed numerical values of any symbol are called a constant.<br \/>i.e.\u00a0 7, 3, -2, 3\/7, etc. are all constants.<\/p>\n<p><strong><b>Variables<\/b><\/strong>: Any symbol that might assign to different numerical values are known as a variable.<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C=2\u03a0r\u00a0\u00a0\u00a0i.e.,\u00a0 (Circumference of a circle)<br \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u201cr \u201c- radius of circle Where 2 as constants. While \u201cC\u201d and \u201cr\u201d are variable<\/p>\n<p><strong><b>Algebraic expressions<\/b><\/strong>: Mixture of constants plus variables. Connected through few or all operations i.e., +, -, x and is known as an algebraic expression.<\/p>\n<p><strong><b>Coefficients:<\/b><\/strong>\u00a0 Within a polynomial x3\u00a0+ 3&#215;2\u00a0+ 3x + 1\u00a0coefficient of\u00a0\u00a0x3, x2, x are 1, 3, 3\u00a0as shown and alongside the constant term in it will be +1.<\/p>\n<p><strong><b>Polynomial degree in one variable:<\/b><\/strong> The maximum power of the variable is known as the degree of the polynomial.<\/p>\n<p><strong><b>Constant polynomial<\/b><\/strong>: Polynomial when containing only one term, consisting of a constant term is called a constant polynomial. The degree of a non-zero constant polynomial is always zero.<\/p>\n<p><strong><b>Zero polynomial<\/b><\/strong>: A polynomial having only a single term, which is zero called a zero polynomial. A zero polynomial degree is not defined.<br \/>Zeros of a polynomial:\u00a0Let us take \u201cp(x)\u201d as a polynomial. Where if\u00a0then we can say the polynomial of p(x) is zero.<\/p>\n<p><strong><b>Remark:<\/b><\/strong>\u00a0Searching zeros of polynomial p(x) ensure solving equations p(x) =0.<\/p>\n<p><strong><b>Remainder theorem<\/b><\/strong>: Let us assume f(x) as a polynomial of degree &gt;0 and consider it as any real number. When f(x) is divided by f(x-a) then the remainder is f(a).\u00a0\u00a0<\/p>\n<p>Use of a\u00a0<strong><b>grouping method<\/b><\/strong><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Whenever a common factor exists between the groupings at that time factor polynomials are used.<\/p>\n<p>The other two methods are by using special factoring formulas where you need to memorize for your exams; they include the formulas for factoring the sums and the differences of cubes. Here are the two formulas:<\/p>\n<p><strong><b>Factoring a Sum of Cubes<\/b><\/strong>:<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0a3\u00a0+ b3\u00a0= (a + b) (a2\u00a0\u2013 ab + b2)<\/p>\n<p><strong><b>F<\/b><\/strong><strong><b>actoring a Difference of Cubes<\/b><\/strong>:<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 a3\u00a0\u2013 b3\u00a0= (a \u2013 b) (a2\u00a0+ ab + b2)<\/p>\n<p>You\u2019ll learn more as you move up in your advanced classes and you will learn how these formulas have come up.<\/p>\n<p>Know more <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">here<\/a>.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rs-aggarwal-chapter-3-class-9-maths-exercises-31-ex-3a-solutions\"><\/span>FAQs on RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions<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-1703048315023\" 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-rs-aggarwal-chapter-3-class-9-maths-exercises-31-ex-3a-solutions\"><\/span>From where can I download the PDF of RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions?<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-1703048329952\" 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-rs-aggarwal-chapter-3-class-9-maths-exercises-31-ex-3a-solutions\"><\/span>How much does it cost to download the PDF of RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions?<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 id=\"faq-question-1703048348073\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-access-the-rs-aggarwal-chapter-3-class-9-maths-exercises-31-ex-3a-solutions-pdf-offline\"><\/span>Can I access the RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions PDF offline?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Once you have downloaded the PDF online, you can access it offline as well.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RS Aggarwal Chapter 3 Class 9 Maths Exercise 3.1 Solutions: Some more algebraic identities are discussed in this chapter. It can be used in the factoring and calculation of some given expressions. Also, this chapter discusses various polynomials based on the number of words. RS Aggarwal Solution for Class 9 Mathematics Solutions Chapter 3 by &#8230; <a title=\"RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions 2024\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rs-aggarwal-chapter-3-class-9-maths-exercise-3-1-solutions\/\" aria-label=\"More on RS Aggarwal Chapter 3 Class 9 Maths Exercises 3.1 (ex 3a) Solutions 2024\">Read more<\/a><\/p>\n","protected":false},"author":236,"featured_media":71994,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73723,73412,73410],"tags":[3081,3086,4711],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71976"}],"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\/236"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=71976"}],"version-history":[{"count":2,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71976\/revisions"}],"predecessor-version":[{"id":524720,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71976\/revisions\/524720"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/71994"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=71976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=71976"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=71976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}