Linear algebra bilinear function

[specialnlovin]

True or false. provide either a proof or counter example accordingly
if f is a function V$$\times$$V$$\rightarrow$$k such that for all v,u,w$$\in$$V, $$\lambda$$$$\in$$k, f($$\lambda$$v+u,w)=$$\lambda$$f(v,w)+f(u,w). Then f is bilinear
I know that this does not include the second part of the requirement to be bilinear, however I cannot come up with a counter example. In order to find a counter example I know I should multiply a linear and non linear transformation but I cannot come up with one that disproves the statement.

 

[Outlined]

what about
$$f : \textbf{R}^{2} \times \textbf{R}^{2} \longrightarrow \textbf{R}$$
$$(u, v) \longmapsto u_{1}$$