Answer
$(x-1)(x+1)(x^4+x^2+1)$
Work Step by Step
Since $x^6 = (x^2)^3$, the given expression is equivalent to:
$=(x^2)^3-1$
The expression above is a difference of two cubes.
Factor using the formula $a^3-b^3=(a-b)(a^2+ab+b^2)$ where $a=x^2$ and $b=1$ to obtain:
$=(x^2-1)[(x^2)^2+x^2(1) + 1^2]
\\=(x^2-1)(x^4+x^2+1)$
The first factor above is a difference of two squares.
Factor using the formula $a^2-b^2=(a-b)(a+b)$ with $a=x$ and $b=1$ to obtain:
$=(x-1)(x+1)(x^4+x^2+1)$
