College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises - Page 68: 80



Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ (\sqrt[3]{7}+3)(\sqrt[3]{7^2}-3\sqrt[3]{7}+9) ,$ use the factoring of the sum of $2$ cubes. $\bf{\text{Solution Details:}}$ Using the factoring of the sum of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2),$ the expression above is equivalent to\begin{array}{l}\require{cancel} (\sqrt[3]{7})^3+(3)^3 \\\\= 7+27 \\\\= 34 .\end{array}.
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