Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.4 Factoring Perfect-Square Trinomials and Differences of Squares - 5.4 Exercise Set: 115

Answer

$(9+b^{2k})(3+b^{k})(3-b^{k})$

Work Step by Step

Using $x^2-y^2=(x+y)(x-y)$ or the factoring of the difference of 2 squares, then the factored form of the given expression, $ 81-b^{4k} ,$ is \begin{array}{l} (9+b^{2k})(9-b^{2k}) \\\\= (9+b^{2k})(3+b^{k})(3-b^{k}) \end{array}
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