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: 25

Answer

$8\left( t-1 \right)(t^2+t+1)$

Work Step by Step

Factoring the $GCF= 8 ,$ the given expression, $ 8t^3-8 ,$ is equivalent to \begin{array}{l} 8(t^3-1) .\end{array} Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $ 8(t^3-1) ,$ is \begin{array}{l} 8\left( t-1 \right)\left[ (t)^2-(t)\left( -1 \right)+\left( -1 \right)^2 \right] \\\\= 8\left( t-1 \right)(t^2+t+1) .\end{array}
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