Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 60

Answer

$2(x+4y)^2$

Work Step by Step

Factoring the $GCF=2$, then the given expression, $ 2x^2+16xy+32y^2 $, is equivalent to $ 2(x^2+8xy+16y^2) $.\\ The two numbers whose product is $ac= 1(16)=16 $ and whose sum is $b= 8 $ are $\{ 4,4 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 2(x^2+8xy+16y^2) $, is \begin{array}{l}\require{cancel} 2(x^2+4xy+4xy+16y^2) \\\\= 2[(x^2+4xy)+(4xy+16y^2)] \\\\= 2[x(x+4y)+4y(x+4y)] \\\\= 2[(x+4y)(x+4y)] \\\\= 2(x+4y)^2 .\end{array}
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