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 - 5.5 Factoring Sums or Differences of Cubes - 5.5 Exercise Set: 38

Answer

$(5c^2-2d^2)(25c^4+10c^2d^2+4d^4)$

Work Step by Step

Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the given expression, $ 125c^6-8d^6 ,$ is \begin{array}{l} (5c^2-2d^2)[ (5c^2)^2-(5c^2)(-2d^2)+(-2d^2)^2] \\\\= (5c^2-2d^2)(25c^4+10c^2d^2+4d^4) .\end{array}
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