$$V[aX+bY]=a^{2}V[X]+b^{2}V[Y]+2abCov[X,Y]$$
where \(Cov[X,Y]\) is the covariance of X and Y.
Proof : Let X, Y be random variables and a, b be any constants.
\begin{eqnarray*}V[aX+bY]&=&E[\{(aX+bY)-E[(aX+bY)]\}^{2}]\\&=&E[\{a(X-E[X])+b(Y-E[Y])\}^{2}]\ \ \ (\text{∵}\ \ E[aX+bY]=aE[X]+bE[Y]\ \ )\\&=&E[a^{2}(X-E[X])^{2}+b^{2}(Y-E[Y])^{2}+2ab(X-E[X])(Y-E[Y])]\\&=&a^{2}V[X]+b^{2}V[X]+2ab Cov[X,Y]\end{eqnarray*}
See also Covariance.