How to factor a nth degree binomial difference?

Question

I know

$$ a^2-b^2 = (a-b)(a+b) $$

and

$$ a^3-b^3 = (a-b)(a^2+ab+b^2) $$

but is there a formula to factor

$$ a^n-b^n=\space ? $$

Thanks!

Answer 1

Hint. One may just expand $$ (a-b)(a^{n-1}+a^{n-2}b+\cdots+ab^{n-2}+b^{n-1}) $$ and observe what happens.

Answer 2

$a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b^1+a^{n-3}b^2+\dots+a^{n-k-1}b^k+\dots+b^{n-1})$