Solve (2)2x^3y+2x^2y^2-12xy^3

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

Factor

$$2xy\left(2x-3y\right)\left(x+2y\right)$$

Solution Steps

Factor out 2.

$$2\left(2x^{3}y+x^{2}y^{2}-6xy^{3}\right)$$

Consider 2x^{3}y+x^{2}y^{2}-6xy^{3}. Factor out xy.

$$xy\left(2x^{2}+xy-6y^{2}\right)$$

Consider 2x^{2}+xy-6y^{2}. Consider 2x^{2}+xy-6y^{2} as a polynomial over variable x.

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

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 2x^{2} and n divides the constant factor -6y^{2}. One such factor is 2x-3y. Factor the polynomial by dividing it by this factor.

$$\left(2x-3y\right)\left(x+2y\right)$$

Rewrite the complete factored expression.

$$2xy\left(2x-3y\right)\left(x+2y\right)$$

Evaluate

$$2xy\left(2x-3y\right)\left(x+2y\right)$$