Factor completely: 36×2 – 49<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To factor the expression ( 36x^2 – 49 ), we recognize that it is a difference of squares<\/strong>. A difference of squares is any expression in the form ( a^2 – b^2 ), which factors as ( (a – b)(a + b) ).<\/p>\n\n\n\n Thus, the factored form of ( 36x^2 – 49 ) is: In algebra, factoring expressions is an essential technique used to simplify polynomials and solve equations. One important pattern to recognize is the difference of squares<\/strong>, which occurs when a binomial is the result of subtracting one square number from another. The general form of a difference of squares is ( a^2 – b^2 ), and it factors neatly into the product of two binomials: ( (a – b)(a + b) ).<\/p>\n\n\n\n In this problem, ( 36x^2 – 49 ), both terms are perfect squares. The term ( 36x^2 ) is the square of ( 6x ), and ( 49 ) is the square of ( 7 ). Once we recognize this, we can apply the difference of squares formula.<\/p>\n\n\n\n Factoring using this pattern simplifies the expression into two linear binomials: ( (6x – 7)(6x + 7) ). This technique is especially useful because it turns a quadratic expression into a product of simpler terms. Factoring helps in solving equations, simplifying expressions, and understanding relationships between variables.<\/p>\n\n\n\n In summary, the factorization process involved recognizing that the expression fits the difference of squares form and applying the appropriate factoring formula. This is a powerful algebraic tool that helps break down more complex polynomials into simpler parts.<\/p>\n","protected":false},"excerpt":{"rendered":" Factor completely: 36×2 – 49 The Correct Answer and Explanation is : To factor the expression ( 36x^2 – 49 ), we recognize that it is a difference of squares. A difference of squares is any expression in the form ( a^2 – b^2 ), which factors as ( (a – b)(a + b) ). […]<\/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-155922","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155922","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=155922"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155922\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=155922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=155922"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=155922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step-by-Step Solution:<\/h3>\n\n\n\n
\n
The given expression ( 36x^2 – 49 ) is a difference of squares because both terms are perfect squares:
[
36x^2 = (6x)^2 \\quad \\text{and} \\quad 49 = 7^2
]<\/li>\n\n\n\n
The formula is:
[
a^2 – b^2 = (a – b)(a + b)
]
Here, ( a = 6x ) and ( b = 7 ). Using the formula, we can factor the expression:
[
36x^2 – 49 = (6x – 7)(6x + 7)
]<\/li>\n<\/ol>\n\n\n\n
[
(6x – 7)(6x + 7)
]<\/p>\n\n\n\nExplanation (300 words):<\/h3>\n\n\n\n