Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.4 - Polynomials - Exercise Set: 76

Answer

$25x^2+70xy+49y^2-4$

Work Step by Step

The given expression can be written as $[(5x+7y)-2][(5x+7y)+2].$ The expression above is of the form $(a-b)(a+b)$. RECALL: (1) $(a-b)(a+b) = a^2-b^2$ (2) $(a+b)^2=a^2+2ab+b^2$ Multiply the expression using formula (1) above with $a=5x+7y$ and $b=2$ to obtain: $=(5x+7y)^2 - 2^2 \\=(5x+7y)^2-4$ Square the binomial using formula (2) with $a=5x$ and $b=7y$ above to obtain: $=(5x)^2+2(5x)(7y)+(7y)^2-4 \\=25x^2+70xy+49y^2-4$
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