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**1. The problem statement, all variables and given/known data**

Show that for every odd positive integer

*n*the following is correct

x

^{n}+ y

^{n}= (x+y)(x

^{n-1}- x

^{n-2}y + x

^{n-3}y

^{2}- ... - xy

^{n-2}+ y

^{n-1})

**2. Relevant equations**

The one above.

**3. The attempt at a solution**

I have an idea about using induction to prove this. My idea is to write the RHS as a sum where k goes from 1 to n, and also write a similar sum where k goes from 1 to (n+2) (the next odd number). But it really have stopped there.

Since my experience with mathematical proofs is pretty nonexistent, I would appreciate any help on how to attack this problem.