Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.7 - Factoring by Special Products - Exercise Set - Page 309: 12



Work Step by Step

The two numbers whose product is $ac= 81(4)=324 $ and whose sum is $b= 36 $ are $\{ 18,18 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 81x^2+36xy+4y^2 $, is \begin{array}{l}\require{cancel} 81x^2+18xy+18xy+4y^2 \\\\= (81x^2+18xy)+(18xy+4y^2) \\\\= 9x(9x+2y)+2y(9y+2y) \\\\= (9x+2y)(9y+2y) \\\\= (9x+2y)^2 .\end{array}
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