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: 79



Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ (\sqrt[3]{11}-1)(\sqrt[3]{11^2}+\sqrt[3]{11}+1) ,$ use the factoring of the difference of $2$ cubes. $\bf{\text{Solution Details:}}$ Using the factoring of the difference of $2$ cubes which is given by $a^3-b^3=(a-b)(a^2+ab+b^2),$ the expression above is equivalent\begin{array}{l}\require{cancel} (\sqrt[3]{11})^3-(1)^3 \\\\= 11-1 \\\\= 10 .\end{array}
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