Solve 3x^3-3x^2y-6xy^2

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

Factor

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

Solution Steps

Factor out 3.

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

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

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

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

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

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 -2y^{2}. One such factor is x-2y. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression.

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

Evaluate

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