Answer
$3(x^{n}-3y^{n})(x^{n}+3y^{n})$
Work Step by Step
$ 3x^{2n}-27y^{2n}\qquad$...factor out the common term, $3$.
$=3(x^{2n}-9y^{2n})\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=3(x^{n}-3y^{n})(x^{n}+3y^{n})$
