Factor y=9x^3-3x^2+81x-27

$y = 9 x^{3} - 3 x^{2} + 81 x - 27$

Factor $3$ out of $9 x^{3} - 3 x^{2} + 81 x - 27$ .

Factor $3$ out of $9 x^{3}$ .

$y = 3 (3 x^{3}) - 3 x^{2} + 81 x - 27$

Factor $3$ out of $- 3 x^{2}$ .

$y = 3 (3 x^{3}) + 3 (- x^{2}) + 81 x - 27$

Factor $3$ out of $81 x$ .

$y = 3 (3 x^{3}) + 3 (- x^{2}) + 3 (27 x) - 27$

Factor $3$ out of $- 27$ .

$y = 3 (3 x^{3}) + 3 (- x^{2}) + 3 (27 x) + 3 (- 9)$

Factor $3$ out of $3 (3 x^{3}) + 3 (- x^{2})$ .

$y = 3 (3 x^{3} - x^{2}) + 3 (27 x) + 3 (- 9)$

Factor $3$ out of $3 (3 x^{3} - x^{2}) + 3 (27 x)$ .

$y = 3 (3 x^{3} - x^{2} + 27 x) + 3 (- 9)$

Factor $3$ out of $3 (3 x^{3} - x^{2} + 27 x) + 3 (- 9)$ .

$y = 3 (3 x^{3} - x^{2} + 27 x - 9)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$y = 3 ((3 x^{3} - x^{2}) + 27 x - 9)$

Factor out the greatest common factor (GCF) from each group.

$y = 3 (x^{2} (3 x - 1) + 9 (3 x - 1))$

Factor.

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

$y = 3 ((3 x - 1) (x^{2} + 9))$

Remove unnecessary parentheses.

$y = 3 (3 x - 1) (x^{2} + 9)$