Solve 8x^4-27xy^3

$$8 x ^ { 4 } - 27 x y ^ { 3 }$$

Factor

$$x\left(2x-3y\right)\left(4x^{2}+6xy+9y^{2}\right)$$

Solution Steps

Factor out x.

$$x\left(8x^{3}-27y^{3}\right)$$

Consider 8x^{3}-27y^{3}. Rewrite 8x^{3}-27y^{3} as \left(2x\right)^{3}-\left(3y\right)^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(2x-3y\right)\left(4x^{2}+6xy+9y^{2}\right)$$

Rewrite the complete factored expression.

$$x\left(2x-3y\right)\left(4x^{2}+6xy+9y^{2}\right)$$

Evaluate

$$x\left(8x^{3}-27y^{3}\right)$$