Solve 2x^3y-10x^2y^2+12xy^3

$$2 x ^ { 3 } y - 10 x ^ { 2 } y ^ { 2 } + 12 x y ^ { 3 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(x^{3}y-5x^{2}y^{2}+6xy^{3}\right)$$

Consider x^{3}y-5x^{2}y^{2}+6xy^{3}. Factor out xy.

$$xy\left(x^{2}-5xy+6y^{2}\right)$$

Consider x^{2}-5xy+6y^{2}. Consider x^{2}-5xy+6y^{2} as a polynomial over variable x.

$$x^{2}-5yx+6y^{2}$$

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

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

Rewrite the complete factored expression.

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

Evaluate

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