Solve 24x^4-3xy^3

$$24 x ^ { 4 } - 3 x y ^ { 3 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(8x^{4}-xy^{3}\right)$$

Consider 8x^{4}-xy^{3}. Factor out x.

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

Consider 8x^{3}-y^{3}. Rewrite 8x^{3}-y^{3} as \left(2x\right)^{3}-y^{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).

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

Rewrite the complete factored expression.

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

Evaluate

$$24x^{4}-3xy^{3}$$