I want to use this theorem I just proved to show this: $cov(X\pm Y, Z)= cov(X,Z) \pm cov(Y,Z)$
For the previous proof I re-wrote both sides in terms of the expected value and show that they were equivalent.
So for this one I would re-write the left hand side to be E((X+Y)(Z+W))-E(X+Y)E(Z+W) Now do I have to re-write the right hand side and manipulate as well? I know there has to be a way to use the theorem I had just proved. Any suggestions?