How to perform commutation of $[A+B, C+D]$? [closed]

I want to know a logical method of performing a commutation for [$$a\hat{A} + b\hat{B}, c\hat{C} + d\hat{D}$$] where $$a$$, $$b$$, $$c$$ and $$d$$ are just constants. I know the rules for [$$\hat{A} + \hat{B}, \hat{C}$$] but cannot seem to apply it for the former mentioned.

Commutator brackets are linear in both slots, so $$[a\hat A+b\hat B,c\hat C +d\hat D]=ac[\hat A,\hat C]+ad[\hat A,\hat D]+bc[\hat B,\hat C]+bd[\hat B,\hat D]$$
This follows from the rule you already know. If $$[\hat A+\hat B,\hat C]=[\hat A,\hat C]+[\hat B,\hat C]$$, then
$$[\hat A,\hat C+\hat D]= -[\hat C + \hat D,\hat A]= -\left([\hat C,\hat A]+[\hat D,\hat A]\right)$$ $$=[\hat A,\hat C]+[\hat A,\hat D]$$