#### Answer

$(\sqrt[3]{a}-4)(\sqrt[3]{a}+5)=\sqrt[3]{a^{2}}+\sqrt[3]{a}-20$

#### Work Step by Step

$(\sqrt[3]{a}-4)(\sqrt[3]{a}+5)$
Evaluate the product:
$(\sqrt[3]{a}-4)(\sqrt[3]{a}+5)=\sqrt[3]{a^{2}}+5\sqrt[3]{a}-4\sqrt[3]{a}-20=...$
Now, simplify by combining like terms:
$...=\sqrt[3]{a^{2}}+(5-4)\sqrt[3]{a}-20=\sqrt[3]{a^{2}}+\sqrt[3]{a}-20$