{"id":238927,"date":"2025-06-18T13:30:56","date_gmt":"2025-06-18T13:30:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238927"},"modified":"2025-06-18T13:30:58","modified_gmt":"2025-06-18T13:30:58","slug":"kuta-software-infinite-algebra-1-factoring-special-cases-factor-each-completely-1-16n2%e2%88%929-3-16b2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/kuta-software-infinite-algebra-1-factoring-special-cases-factor-each-completely-1-16n2%e2%88%929-3-16b2\/","title":{"rendered":"Kuta Software – Infinite Algebra 1 Factoring Special Cases Factor each completely. 1)\u00a016n2\u22129\u00a03)\u00a016b2"},"content":{"rendered":"\n
Kuta Software - Infinite Algebra 1 Factoring Special Cases Factor each completely. 1)\u00a016n2\u22129\u00a03)\u00a016b2

<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
The given expression to factor is 16n\u00b2 – 9.<\/p>\n\n\n\n
Recognizing this as a difference of squares, we apply the formula a\u00b2 – b\u00b2 = (a + b)(a – b). In this case, 16n\u00b2 is a perfect square, written as (4n)\u00b2, and 9 is also a perfect square, written as 3\u00b2. Using the formula, we factor the expression as follows:<\/p>\n\n\n\n
16n\u00b2 – 9 = (4n + 3)(4n – 3)<\/p>\n\n\n\n
Explanation:<\/p>\n\n\n\n
To solve this problem, we first identify whether the given polynomial fits a recognizable factoring pattern. The expression 16n\u00b2 – 9 consists of two terms, and both are perfect squares. The first term, 16n\u00b2, can be rewritten as (4n)\u00b2, while the second term, 9, is rewritten as 3\u00b2. Since the expression is written in the form a\u00b2 – b\u00b2, we apply the difference of squares formula, which states that a\u00b2 – b\u00b2 factors into (a + b)(a – b).<\/p>\n\n\n\n
We proceed by setting a = 4n and b = 3. Substituting these values into the formula, we obtain:<\/p>\n\n\n\n
(4n)\u00b2 – 3\u00b2 = (4n + 3)(4n – 3)<\/p>\n\n\n\n
This method simplifies the given quadratic expression into a product of two binomials. Factoring through the difference of squares is useful because it allows algebraic expressions to be broken down into simpler multiplicative components, making further calculations and problem-solving easier. In mathematics, recognizing special factoring cases like the difference of squares helps in solving equations efficiently without resorting to complex methods such as the quadratic formula. The difference of squares appears frequently in algebra and higher-level mathematics, making it an essential skill for polynomial manipulation and simplification.<\/p>\n\n\n\n
Thus, the completely factored form of the given expression is (4n + 3)(4n – 3).<\/p>\n\n\n\n
\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
Kuta Software – Infinite Algebra 1 Factoring Special Cases Factor each completely. 1)\u00a016n2\u22129\u00a03)\u00a016b2 The Correct Answer and Explanation is: The given expression to factor is 16n\u00b2 – 9. Recognizing this as a difference of squares, we apply the formula a\u00b2 – b\u00b2 = (a + b)(a – b). In this case, 16n\u00b2 is a perfect […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-238927","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238927","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=238927"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238927\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238927"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238927"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238927"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}