Answer
$\sqrt[3]{a^2}+9\sqrt[3]{a}+14$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, then,
\begin{array}{l}
\left( \sqrt[3]{a}+2 \right)\left( \sqrt[3]{a}+7 \right)
\\=
(\sqrt[3]{a})(\sqrt[3]{a})+(\sqrt[3]{a})(7)+(2)(\sqrt[3]{a})+(2)(7)
\\=
\sqrt[3]{a^2}+7\sqrt[3]{a}+2\sqrt[3]{a}+14
\\=
\sqrt[3]{a^2}+9\sqrt[3]{a}+14
.\end{array}