Answer
$(3x-1)(9x^{2} + 3x + 1)$
Work Step by Step
$ 27x^{3}-1\qquad$...recognize the difference of two cubes: $\mathrm{A}^{3}-\mathrm{B}^{3} = (\mathrm{A}-\mathrm{B})(\mathrm{A}^{2} + \mathrm{A}\mathrm{B} + B^{2})$
$=(3x)^{3}-1^{3}$
$=(3x-1)((3x)^{2} + 3x + 1^{2})$
$=(3x-1)(9x^{2} + 3x + 1)$
