Let A and B be two observables that both commute with their commutator [A,B].

a) Show, e.g., by induction, that [A,B^{n}]=nB^{n-1}[A,B].

Prove for n=1

[A,B^{1}]=1B^{1-1}[A,B].

[A,B]=B^{0}[A,B]=[A,B]

Show that it is true for n+1

[A,B^{n+1}]=[A,B^{n}B]=B^{n}[A,B]+[A,B^{n}]B

I am not sure how to continue. Could someone give me a hint what I should do next?

Thank you.