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: 11

Answer

$(4x-7y)^2$

Work Step by Step

The two numbers whose product is $ac= 16(49)=784 $ and whose sum is $b= -56 $ are $\{ -28,-28 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 16x^2-56xy+49y^2 $, is \begin{array}{l}\require{cancel} 16x^2-28xy-28xy+49y^2 \\\\= (16x^2-28xy)-(28xy-49y^2) \\\\= 4x(4x-7y)-7y(4x-7y) \\\\= (4x-7y)(4x-7y) \\\\= (4x-7y)^2 .\end{array}
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