Solve 2uv^3-98u^3v

$$2 u v ^ { 3 } - 98 u ^ { 3 } v$$

Factor

$$2uv\left(v-7u\right)\left(7u+v\right)$$

Solution Steps

Factor out 2.

$$2\left(uv^{3}-49u^{3}v\right)$$

Consider uv^{3}-49u^{3}v. Factor out uv.

$$uv\left(v^{2}-49u^{2}\right)$$

Consider v^{2}-49u^{2}. Rewrite v^{2}-49u^{2} as v^{2}-\left(7u\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-7u\right)\left(v+7u\right)$$

Reorder the terms.

$$\left(-7u+v\right)\left(7u+v\right)$$

Rewrite the complete factored expression.

$$2uv\left(-7u+v\right)\left(7u+v\right)$$

Evaluate

$$2uv\left(v^{2}-49u^{2}\right)$$