The best linear predictor of Y with respect to $\displaystyle X_1$ and $\displaystyle X_2$ is equal to $\displaystyle a + bX_1 + cX_2$, where a, b and c are chosen to minimise

$\displaystyle E[(Y - (a +bX_1 +cX_2))^2]$

I get

$\displaystyle E[Y^2 -2aY - 2bX_1Y - 2cX_2Y + a^2 + 2abX_1 +2acX_2 +2bcX_1X_2 + b^2X_1^2 + c^2X_2^2]$

but cannot see where to go next