Answer :
[tex]x\times\frac{1}{3}(x\times\frac{1}{2}+2x^2)=\frac{x}{3}\times(\frac{x}{2}+2x^2)[/tex]
Open the bracket in the above expression.
[tex]\begin{gathered} \frac{x}{3}\times(\frac{x}{2}+2x^2)=\frac{x}{3}\times\frac{x}{2}+\frac{x}{3}\times2x^2 \\ =\frac{x^2}{2\times3}+\frac{2x^3}{3} \\ =\frac{x^2}{6}+\frac{2x^3}{3} \\ =\frac{2}{3}x^3+\frac{1}{6}x^2 \end{gathered}[/tex]Thus, the simplest form of the given expression is,
[tex]\frac{2}{3}x^3+\frac{1}{6}x^2[/tex]