Assuming that random variables X and Y are independent, what is $\displaystyle Var((1+X)(1+Y)-1)=Var(X+Y+XY)$?

Should I start as follows \begin{equation} Var((1+X)(1+Y)-1)\\ =Var((1+X)(1+Y))\\ =(E[(1+X)])^2 Var(1+Y)+(E[(1+Y])^2 Var(1+X)+Var(1+X)Var(1+Y) \end{equation}

or maybe as follows

\begin{equation} \\ Var((1+X)(1+Y)-1)\\ =Var(1+Y+X+XY-1)\\ =Var(X+Y+XY)\\ =Var(X)+Var(Y)+Var(XY)+2Cov(X,Y)+2Cov(X,XY)+2Cov(Y,XY) \end{equation}

I'm considering could I express the problem in terms of covariances (and variances) between individual random variables. I would like to forecast the variance by individual covariances in my model if its possible. Does to solution simplify if expected values of the variables are zero?