I'm having trouble figuring out the following commutator relation problem:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose A and B commute with their commutator, i.e., [tex][B,[A,B]]=[A,[A,B]]=0[/tex]. Show that

[tex][A,B^{n}]=nB^{n-1}[A,B][/tex]

I have

[tex][A,B^{n}] = AB^{n} - B^{n}A[/tex]

and also

[tex][A,B^{n}] = AB^{n} - B^{n}A = ABB^{n-1} - BB^{n-1}A[/tex]

I don't know where to go from here. I'm not positive the above relation is correct either.

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# Show that [A,B^{n}]=nB^{n-1}[A,B]

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