Answer
$1-\sqrt[3]{12}+\sqrt[3]{18}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, then,
\begin{array}{l}
\left( \sqrt[3]{3}+\sqrt[3]{2} \right)\left( \sqrt[3]{9}-\sqrt[3]{4} \right)
\\=
(\sqrt[3]{3})(\sqrt[3]{9})+(\sqrt[3]{3})(-\sqrt[3]{4})+(\sqrt[3]{2})(\sqrt[3]{9})+(\sqrt[3]{2})(-\sqrt[3]{4})
\\=
\sqrt[3]{27}-\sqrt[3]{12}+\sqrt[3]{18}-\sqrt[3]{8}
\\=
3-\sqrt[3]{12}+\sqrt[3]{18}-2
\\=
1-\sqrt[3]{12}+\sqrt[3]{18}
.\end{array}
