(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the following when p is a positive integer:

[tex]b^p - a^p = (b-a)(b^{p-1}+b^{p-2}a+b^{p-3}a^2+...+ba^{p-2}+a^{p-1})[/tex]

Hint: Use the telescoping property for sums.

2. Relevant equations

None

3. The attempt at a solution

I tried reducing it to, [tex](b-a)\sum_{k=1}^p b^{p-k}a^{k-1}[/tex] but I wasn't able to do anything with it.

I've been trying to work on this exercise which is a part of a problem set in induction. But I've been having quite a bit of difficulty and I'd appreciate it if somebody here could give me a hint as to the general direction. It's been bugging me for the past few days.

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# Homework Help: Help proving polynomial identity

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