$G$ is Lie group and $V$ is a representations of $G$,prove representations $V \otimes V \cong S^2(V) \oplus \Lambda^2(V)$

Question

Let $G$ a Lie group and let $V$ a representations of $G$. Then we have the following representations are isomorphic: \begin{align} V \otimes V \cong S^2(V) \oplus \Lambda^2(V) \end{align}

I have no idea how to prove this fact. Any suggestions? Thanks in advance!