Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 3 - Exponents, Polynomials and Functions - 3.5 Special Factoring Techniques - 3.5 Exercises: 61

Answer

$(5x-4)(25x^2+20x+16)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 125x^3-64 ,$ use the factoring of the sum or difference of $2$ cubes. $\bf{\text{Solution Details:}}$ The expressions $ 125x^3 $ and $ 64 $ are both perfect cubes (the cube root is exact). Hence, $ 125x^3-64 $ 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} (5x)^3-(4)^3 \\\\= (5x-4)[(5x)^2+5x(4)+(4)^2] \\\\= (5x-4)(25x^2+20x+16) .\end{array}
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