Solve 3ab^3-3a^3b

$$3 a b ^ { 3 } - 3 a ^ { 3 } b$$

Factor

$$3ab\left(b-a\right)\left(a+b\right)$$

Solution Steps

Factor out 3.

$$3\left(ab^{3}-a^{3}b\right)$$

Consider ab^{3}-a^{3}b. Factor out ab.

$$ab\left(b^{2}-a^{2}\right)$$

Consider b^{2}-a^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(b-a\right)\left(b+a\right)$$

Reorder the terms.

$$\left(-a+b\right)\left(a+b\right)$$

Rewrite the complete factored expression.

$$3ab\left(-a+b\right)\left(a+b\right)$$

Evaluate

$$3ab\left(b^{2}-a^{2}\right)$$