Factor 3x^3-2y^3-6x^2y^2+xy

$3 x^{3} - 2 y^{3} - 6 x^{2} y^{2} + x y$

Regroup terms.

$- 6 x^{2} y^{2} + 3 x^{3} - 2 y^{3} + x y$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Factor $- 1$ out of $- 2 y^{2} + x$ .

Factor $- 1$ out of $- 2 y^{2}$ .

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

Factor $- 1$ out of $x$ .

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

Factor $- 1$ out of $- (2 y^{2}) - 1 (- x)$ .

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