Proving the factorization of xn + yn for odd n

[Abst.nonsense]

Homework Statement

Show that for every odd positive integer n the following is correct

xⁿ + yⁿ = (x+y)(x^n-1 - x^n-2y + x^n-3y² - ... - xy^n-2 + y^n-1)

Homework Equations

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.

 

[HallsofIvy]

No need to use induction, just go ahead and multiply out the right hand side.