When can you factor out terms from commutators like [AB,C]?

[Dishsoap]

This is not a homework question, I just can't find a good resource on this topic.

I am working in quantum mechanics on commutator relations. My book (Griffiths) lacks information on how to manipulate the commutator relations.

For instance, when I have [AB,C], when can I make it A[B,C]? Or is it A[B,C]+[B,C]A? I can't find an online resource that explains these things. Help please!

 

[unscientific]

This is not a homework question, I just can't find a good resource on this topic.

I am working in quantum mechanics on commutator relations. My book (Griffiths) lacks information on how to manipulate the commutator relations.

For instance, when I have [AB,C], when can I make it A[B,C]? Or is it A[B,C]+[B,C]A? I can't find an online resource that explains these things. Help please!

Do things like the product rule in differentiation:

[AB,C] = [A,C]B + A[B,C]