Alternating bilinear form with wedge product. equality problem

Question

Let $\phi : \textbf{R}^4 \otimes \textbf{R}^4 \rightarrow \textbf{R}$ be an alternating bilinear form.

Prove that there exist linear maps $\alpha, \beta :\textbf{R}^4 \rightarrow \textbf{R}$ with $\phi = \alpha \wedge \beta$ if and only if $\phi \wedge \phi = 0$

Can somebody help me solving this one?

Thank you.