Expand and simplify (2x + 5)^2<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: {4x^2 + 20x + 25}<\/strong><\/mark><\/p>\n\n\n\n To expand and simplify ((2x + 5)^2), we can use the formula for the square of a binomial, which states that ((a + b)^2 = a^2 + 2ab + b^2). In our case, (a = 2x) and (b = 5).<\/p>\n\n\n\n We can set:<\/p>\n\n\n\n Using the binomial square formula, we have:<\/p>\n\n\n\n [ Now we can combine all the calculated terms:<\/p>\n\n\n\n [ Thus, the expanded form of ((2x + 5)^2) is:<\/p>\n\n\n\n [ In the expansion of a binomial, we are effectively multiplying the binomial by itself. The binomial formula helps us to organize this multiplication systematically. Each term in the binomial is multiplied by every other term, ensuring that we account for all possible products.<\/p>\n\n\n\n Here, squaring the first term ((2x)) gives us the leading term of the polynomial. The middle term arises from the product of the two terms multiplied by two, as we are combining the effects of both terms on each other. The last term is the square of the constant, giving the polynomial a constant component.<\/p>\n\n\n\n This process illustrates the principles of polynomial expansion and showcases how algebraic identities can simplify calculations, making them less prone to error and more efficient.<\/p>\n","protected":false},"excerpt":{"rendered":" Expand and simplify (2x + 5)^2 The Correct Answer and Explanation is : The correct answer is: {4x^2 + 20x + 25} To expand and simplify ((2x + 5)^2), we can use the formula for the square of a binomial, which states that ((a + b)^2 = a^2 + 2ab + b^2). In our case, […]<\/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-152576","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152576","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=152576"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152576\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Identify (a) and (b)<\/h3>\n\n\n\n
\n
Step 2: Apply the Binomial Square Formula<\/h3>\n\n\n\n
(2x + 5)^2 = (2x)^2 + 2(2x)(5) + (5)^2
]<\/p>\n\n\n\nStep 3: Calculate Each Term<\/h3>\n\n\n\n
\n
[
(2x)^2 = 4x^2
]<\/li>\n\n\n\n
[
2(2x)(5) = 20x
]<\/li>\n\n\n\n
[
(5)^2 = 25
]<\/li>\n<\/ol>\n\n\n\nStep 4: Combine All Terms<\/h3>\n\n\n\n
(2x + 5)^2 = 4x^2 + 20x + 25
]<\/p>\n\n\n\nFinal Result<\/h3>\n\n\n\n
\\boxed{4x^2 + 20x + 25}
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n