Answer
$\sqrt[3]{a^2}+\sqrt[3]{a}-20$
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}-4 \right)\left( \sqrt[3]{a}+5 \right)
\\=
(\sqrt[3]{a})(\sqrt[3]{a})+(\sqrt[3]{a})(5)+(-4)(\sqrt[3]{a})+(-4)(5)
\\=
\sqrt[3]{a^2}+5\sqrt[3]{a}-4\sqrt[3]{a}-20
\\=
\sqrt[3]{a^2}+\sqrt[3]{a}-20
.\end{array}