Factor 6-9x^2+12y-18x^2y

$6 - 9 x^{2} + 12 y - 18 x^{2} y$

Step 1

Factor $3$ out of $6 - 9 x^{2} + 12 y - 18 x^{2} y$ .

Factor $3$ out of $6$ .

$3 (2) - 9 x^{2} + 12 y - 18 x^{2} y$

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

$3 (2) + 3 (- 3 x^{2}) + 12 y - 18 x^{2} y$

Factor $3$ out of $12 y$ .

$3 (2) + 3 (- 3 x^{2}) + 3 (4 y) - 18 x^{2} y$

Factor $3$ out of $- 18 x^{2} y$ .

$3 (2) + 3 (- 3 x^{2}) + 3 (4 y) + 3 (- 6 x^{2} y)$

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

$3 (2 - 3 x^{2}) + 3 (4 y) + 3 (- 6 x^{2} y)$

Factor $3$ out of $3 (2 - 3 x^{2}) + 3 (4 y)$ .

$3 (2 - 3 x^{2} + 4 y) + 3 (- 6 x^{2} y)$

Factor $3$ out of $3 (2 - 3 x^{2} + 4 y) + 3 (- 6 x^{2} y)$ .

$3 (2 - 3 x^{2} + 4 y - 6 x^{2} y)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((2 - 3 x^{2}) + 4 y - 6 x^{2} y)$

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

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

Step 3

Factor.

Factor the polynomial by factoring out the greatest common factor, $2 - 3 x^{2}$ .

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

Remove unnecessary parentheses.

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