Factorize `1+x^4+x^8`

Explanation

`1 + x^4 + x^8`

`= 1+ x^4 + x^8 + x^4 - x^4`

using `x^8 = x^4*x^4= (x^4)^2`

`= 1 + 2x^4 + x^8 - x^4`

using `(a+b)^2 = a^2 + 2ab + b^2`

`(1)^2 + 2*1*(x^4) + (x^4)^2 - x^4`

`= (x^4+1)^2 - x^4`

`= (x^4 + 1)^2 - (x^2)^2`

...