Answer
$(1+4x^{6}y^{6})(1+2x^{3}y^{3})(1-2x^{3}y^{3})$
Work Step by Step
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, then the factored form of the given expression, $
1-16x^{12}y^{12}
$, is
\begin{array}{l}
(1+4x^{6}y^{6})(1-4x^{6}y^{6})
\\\\=
(1+4x^{6}y^{6})(1+2x^{3}y^{3})(1-2x^{3}y^{3})
.\end{array}