Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Mixed Review Exercises: 4

Answer

$(2-a)(4+2a+a^2)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 8-a^3 ,$ use the factoring of the sum/difference of $2$ cubes. $\bf{\text{Solution Details:}}$ The expressions $ 8 $ and $ a^3 $ are both perfect cubes (the cube root is exact). Hence, $ 8-a^3 $ is a $\text{ difference }$ of $2$ cubes. Using the factoring of the sum or difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2)$ the expression above is equivalent to \begin{array}{l}\require{cancel} (2)^3-(a)^3 \\\\= (2-a)[(2)^2+2(a)+(a)^2] \\\\= (2-a)(4+2a+a^2) .\end{array}
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