Solve the commutator relations

Hello, I need to solve the commutator relations above. I found the equation above for the last one, but I am not sure, if something similar applys to the first one. I am a little bit confused, because I know there has to be a trick and you don't solve it like other commutator.
Thanks for your help!

Are you familiar with the expansion of a commutator on the form ##[AB,C]##? If not, take the time to write it out and see if you can express it in terms of commutators containing only two operators.

You understand, of course, that the relevant equation is what you need to prove. You can do this using mathematical induction and the identity suggested by @Orodruin.