Answer
$34$
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}.
