Intermediate Algebra (6th Edition)

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

Chapter 6 - Cumulative Review - Page 408: 41

Answer

$(x+2+y)(x+2-y)$

Work Step by Step

The first $3$ terms of the given expression, $ x^2+4x+4-y^2 ,$ is a perfect square trinomial. Hence, the factored form is \begin{array}{l}\require{cancel} (x+2)^2-y^2 .\end{array} Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the sum and difference of like terms, then the completely factored form of the expression, $ (x+2)^2-y^2 ,$ is \begin{array}{l}\require{cancel} [(x+2)+y][(x+2)-y] \\\\= (x+2+y)(x+2-y) .\end{array}
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