College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.4 - Factoring Polynomials - R.4 Exercises - Page 40: 94

Answer

$(b+4-a)(b+4+a)$

Work Step by Step

The first $3$ terms of the given expression, $ b^2+8b+16-a^2 ,$ is a perfect square trinomial. Hence, the factored form is \begin{array}{l}\require{cancel} (b^2+8b+16)-a^2 \\\\= (b+4)^2-a^2 .\end{array} Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of two squares, then the factored form of the expression, $ (b+4)^2-a^2 ,$ is \begin{array}{l}\require{cancel} [(b+4)-a][(b+4)+a] \\\\= (b+4-a)(b+4+a) .\end{array}
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