Proving End_A (A') for additive category A' has ring structure

Question

I am currently trying to prove that if $A$ is an additive category and $A'$ is an object, then $End_A (A')$ has a natural ring structure. The only part I am not sure about is proving the distributive property. It seems clear that I have to use the fact that composition is bilinear. However, my understanding of bilinearity is that it is just the distributive property. Am I correct?