Solve 10xy^4-10x^4y

$$10 x y ^ { 4 } - 10 x ^ { 4 } y$$

Factor

$$10xy\left(y-x\right)\left(x^{2}+xy+y^{2}\right)$$

Solution Steps

Factor out 10.

$$10\left(xy^{4}-x^{4}y\right)$$

Consider xy^{4}-x^{4}y. Factor out xy.

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

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

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

Rewrite the complete factored expression.

$$10xy\left(-x+y\right)\left(x^{2}+xy+y^{2}\right)$$

Evaluate

$$10xy\left(y^{3}-x^{3}\right)$$