Elementary Algebra

Published by Cengage Learning

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2: 89

Answer

$(3a-4b)(9a^2+12ab+16b^2)$

Work Step by Step

Using $a^3-b^3=(a-b)(a^2+ab+b^2)$, or the factoring of the difference of $2$ cubes, the factored form of the given expression, $27a^3-64b^3 ,$ is \begin{array}{l}\require{cancel} (3a-4b)[(3a)^2+3a(4b)+(4b)^2] \\\\= (3a-4b)(9a^2+12ab+16b^2) .\end{array}

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