factoring x^6 - 1?

x^6 - 1
= (x^3 + 1)(x^3 - 1)
= (x + 1)(x^2 - x + 1)(x - 1)(x^2 + x + 1)

Writing x^6 as (x^3)^2

and 1 as 1*1

this expression is the difference of two squares

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

Therefore, the expression factors as

(x^3 + 1)(x^3 - 1)

x^6 - 1

(x^3-1)(x^3+1)

(x-1)(x^2 - x + 1)(x^3+1)