Let $X\sim N(12,4)$ and $Y \sim N(3,1)$
Let $Z = X - Y$
Find the Moment Generating Function of $Z$.
I tried finding the expected value of $e$ to the power of $tz$, but this isn't possible to separate in the expected value function. I know how to use find the MGF when it is a sum of 2 random variables, but what is the technique when it is a difference like this?