We derive and describe the factorizations for a difference $a^n-b^n$ or sum $a^n+b^n$ of two same powers. In particular, this generalizes the famous and useful difference of squares factorization $$a^2-b^2=(a-b)(a+b).$$
We derive and describe the factorizations for a difference $a^n-b^n$ or sum $a^n+b^n$ of two same powers. In particular, this generalizes the famous and useful difference of squares factorization $$a^2-b^2=(a-b)(a+b).$$