Let $(M_n)_{n\in\mathbb{N}}$ be a discrete martingale with $M_n \in L^2\ \forall n\in\mathbb{N}$ and $S,T$ bounded stopping times with $S\leq T$ a.s.. Show $$E[(M_T − M_S)^2|\mathcal{F_s}]= E[M_T^2 − M_S^2|\cal{F_s}]\ a.s.$$
I tried $$E[(M_T − M_S)^2|\mathcal{F_s}]=E[(M_T^2 -2M_TM_S + M_S^2)^2|\mathcal{F_s}]= E[M_T^2|\mathcal{F_s}]-2E[M_TM_S|\mathcal{F_s}]+E[M_S^2|\mathcal{F_s}]$$ but it does not seem very useful...
I really don't know what to do now. Thanks for any help!!