Question 1121125

Hello, I need help with factoring binomials. I was given problems such as x^7 + y^7 and w^12 - z^12, but I don't know how to solve these. I know how to solve simpler problems such as x^3 - 125, but when I get problems with higher exponents I get confused. Can someone explain the process of solving them? Thank you in advance to anyone who is willing to help. 
<pre>The 2nd polynomial, when factored, should result in: {{{highlight_green(
(w - z)(w + z)(w^2 + z^2)(w^2 + wz + z^2)(w^2 - wz + z^2)(w^4 - w^2z^2 + z^4)))}}} after first applying 
DIFFERENCE of TWO SQUARES (DOTS) to the given binomial, and then DIFFERENCE of TWO CUBES (DOTC) to 1 binomial, and finally, SUM of TWO CUBES to 2 other binomials.