I came across the following problem in class and my teacher was unable to help. The problem was factorise $x^6 - 1$, if you used the difference of 2 squares then used the sum and difference of 2 cubes you came out with the following factorisation; $(x-1)(x+1)(x^2 +x + 1)(x^2 - x + 1)$. However if you used the sum and difference of 2 cubes first you factorised to the following; $(x-1)(x+1)(x^4 + x^2 + 1)$. How would I factorise further from there?
How do you factorise $x^4 + x^2 + 1$?