## College Algebra (11th Edition)

$34$
$\bf{\text{Solution Outline:}}$ 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}.