I just cant get it right.
Prove $<x,y> = \frac{1}{4} \sum_{\lambda^4 = 1} \lambda ||\lambda x+y||^2$
$$\lambda ||\lambda x+y||^2 = \lambda<\lambda x+y,\lambda x+y> = \lambda(<\lambda x,\lambda x>+<\lambda x,y>+<y,\lambda x>+<y,y>)$$
$=\lambda(||x||^2 + \bar\lambda<x,y>+\lambda<y,x>+||y||^2) = \lambda||x||^2 + <x,y>-<y,x>+\lambda||y||^2 $
$= \lambda(||x||^2+||y||^2) + <x,y>-<y,x>$
Im missing something but i dont know where