Let V be a real inner product space. Show that

$\displaystyle (x , y) = \frac{1}{4}(||x + y||^2 - ||x - y||^2)$

for all $\displaystyle x , y \in V$.

Not really sure where to start with this...

Do i start by proving that (x , y) = (y , x)? which i can see because of the absolute value signs (is that what the || lines are called..?) that it is.

Then is it just showing that $\displaystyle \lambda x + \mu y , z = \lambda (x,z) + \mu (y,z)$

and also

(x , x) = 0