I have standard normally distributed random variables $X, Y, V, Z$ and want to find $$Var(XY + VZ)$$ but have the following conditions: $$Cov(Y,Z)>0$$ $$Cov(X,Y)=Cov(X,V)=Cov(X,Z)=Cov(Y,V)=Cov(V,Z)=0$$
That is, the multiplicands $Y$ and $Z$ are dependent. I assume this complicates the proposed variance, but am unsure how to proceed.