How to prove that if for $\displaystyle ( \mathbb{R}^n , \ || \ * \ ||) $ is $\displaystyle ||x+y||^2+||x-y||^2=2(||x||^2+||y||^2) $ then we can define a dot product as $\displaystyle <x,y>=\frac{||x+y||^2-||x-y||^2}{4}$? Intuitionly it is true but I have great problem with proof of bilinear of it. It doesn't seem so simple. Any clues?