College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.4: 84

Answer

$40xy$

Work Step by Step

$$(5x+2y)^2-(5x-2y)^2$$ First square each binomial. To square a binomial, use the formulas $(a+b)^2 = a^2+2ab+b^2$ and $(a-b)^2 = a^2-2ab+b^2$: $$=(5x)^2+2(5x)(2y)+(2y)^2 -[(5x)^2-2(5x)(2y)+(2y)^2]$$ $$=25x^2+20xy+4y^2-(25x^2-20xy+4y^2)$$ $$=25x^2+20xy+4y^2-25x^2+20xy-4y^2$$ $$=40xy$$
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