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: 72

Answer

$(2y+3x)(8y-9x)$

Work Step by Step

The two numbers whose product is $ac= 3(-27)=-432 $ and whose sum is $b= 6 $ are $\{ 24,-18 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 16y^2+6yx-27x^2 $, is \begin{array}{l}\require{cancel} 16y^2+24yx-18yx-27x^2 \\\\= (16y^2+24yx)-(18yx+27x^2) \\\\= 8y(2y+3x)-9x(2y+3x) \\\\= (2y+3x)(8y-9x) .\end{array}
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