Answer
$x\sqrt[3]{2}$
Work Step by Step
Factor each radicand (expression inside the radical sign) so that one of the factors is a perfect square to obtain:
\begin{align*}
&=\sqrt[3]{27x^3(2)}-\sqrt[3]{8x^3(2)}\\
&=\sqrt[3]{(3x)^3(2)}-\sqrt[3]{(2x)^3(2)}\\
\end{align*}
Simplify each radical to obtain:
\begin{align*}
&=3x\sqrt[3]{2}-2x\sqrt[3]{2}\\
\end{align*}
Combine like terms:
\begin{align*}
&=(3x-2x)(\sqrt[3]{2})\\
&=x\sqrt[3]{2}
\end{align*}
