Polarization Identity/Real Vector Space

Theorem
Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space over $\R$.

Let $\norm \cdot$ be the inner product norm for $V$.

Then we have:


 * $4 \innerprod x y = \norm {x + y}^2 - \norm {x - y}^2$

for all $x, y \in V$.

Proof
We have: