Show that for every odd positive integer n the following is correct
xn + yn = (x+y)(xn-1 - xn-2y + xn-3y2 - ... - xyn-2 + yn-1)
The one above.
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.