What is the best way to prove the polarization identity in the following form: for any $u, v \in V$ $$4 \langle T(u), v \rangle = \langle T(u+v), u+v \rangle - \langle T(u-v), u-v \rangle + i\langle T(u+iv), u+iv \rangle - i\langle T(u-iv), u-iv \rangle$$
Here $T$ is a linear operator.
Context
Polarization identity is a useful result in Hilbert spaces. It expresses the inner product in terms of norm:
$$4 \langle u, v \rangle = \langle u+v, u+v \rangle - \langle u-v, u-v \rangle + i\langle u+iv, u+iv \rangle - i\langle u-iv, u-iv \rangle$$
where all terms on the right are just norms squared.
More generally, it gives a way to estimate a bilinear form $B(u,v) = \langle T(u), v \rangle $ in terms of quadratic form $Q(u)=B(u,u)$. This is the generalized form with $T$ above.