Prove that $u\cdot v = 1/4||u+v||^2 - 1/4||u-v||^2$ for all vectors $u$ and $v$ in $\mathbb{R}^n$ I need some help figuring out how to work through this problem.

Prove that $ u \cdot v  = 1/4 ||u + v||^2 - 1/4||u - v||^2$ for all vectors $u$ and $v$ in $\mathbb{R}^n$. 

Sorry, forgot to include my work so far:
I decided to ignore the 1/4 and deal with it later once I had a better understanding of the question.
$= ||u+v||^2 - ||u-v||^2$
$= (u+v)(u+v) - (u-v)(u-v)$
$= u(u+v) + v(u+v) - u(u-v) + v(u-v)$
$= uu + uv + uv + vv - uu + uv + uv - vv$
$u \cdot v= 3(uv)$
This is as far as I've gotten, not sure if I'm on the right track or where to go next.

Remember $\vec{x} \cdot \vec{x} = \left \| x \right \|^2 $. That should be really helpful, in my mind. 
And as @T.Bongers said, when working with identities like this, begin with the harder side. Try to "simplify" it (or make it a big more complex before having things cancel!) into the more basic side. 
