Solve 3x^3-243xy^2

$$3 x ^ { 3 } - 243 x y ^ { 2 }$$

Factor

$$3x\left(x-9y\right)\left(x+9y\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{3}-81xy^{2}\right)$$

Consider x^{3}-81xy^{2}. Factor out x.

$$x\left(x^{2}-81y^{2}\right)$$

Consider x^{2}-81y^{2}. Rewrite x^{2}-81y^{2} as x^{2}-\left(9y\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-9y\right)\left(x+9y\right)$$

Rewrite the complete factored expression.

$$3x\left(x-9y\right)\left(x+9y\right)$$

Evaluate

$$3x\left(x^{2}-81y^{2}\right)$$