Solve 2x^3-18x-x^2y+9y

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

Factor

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

Solution Steps

Do the grouping 2x^{3}-18x-x^{2}y+9y=\left(2x^{3}-18x\right)+\left(-x^{2}y+9y\right), and factor out 2x in the first and -y in the second group.

$$2x\left(x^{2}-9\right)-y\left(x^{2}-9\right)$$

Factor out common term x^{2}-9 by using distributive property.

$$\left(x^{2}-9\right)\left(2x-y\right)$$

Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Rewrite the complete factored expression.

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

Evaluate

$$\left(2x-y\right)\left(x^{2}-9\right)$$