Solve 2p^3q-4pq^3-5pq^3+7p^3q

$$2 p ^ { 3 } q - 4 p q ^ { 3 } - 5 p q ^ { 3 } + 7 p ^ { 3 } q$$

Factor

$$9pq\left(p-q\right)\left(p+q\right)$$

Solution Steps

Factor out pq.

$$pq\left(2p^{2}-4q^{2}-5q^{2}+7p^{2}\right)$$

Consider 2p^{2}-4q^{2}-5q^{2}+7p^{2}. Multiply and combine like terms.

$$9p^{2}-9q^{2}$$

Consider 9p^{2}-9q^{2}. Factor out 9.

$$9\left(p^{2}-q^{2}\right)$$

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

$$\left(p-q\right)\left(p+q\right)$$

Rewrite the complete factored expression.

$$9pq\left(p-q\right)\left(p+q\right)$$

Evaluate

$$9pq\left(p^{2}-q^{2}\right)$$