Answer
$(x-1)(x+1)(x^2+1)(x^8+x^4+1)$
Work Step by Step
Using $a^2-b^2=(a+b)(a-b)$ and $a^3-b^3=(a-b)(a^2+ab+b^2)$, then the given expression, $
x^{12}-1
$, is equivalent to
\begin{array}{l}
(x^4)^3-1^3
\\\\=
[(x^4)-1][(x^4)^2+x^4+1]
\\\\=
(x^4-1)(x^8+x^4+1)
\\\\=
(x^2-1)(x^2+1)(x^8+x^4+1)
\\\\=
(x-1)(x+1)(x^2+1)(x^8+x^4+1)
.\end{array}
