Solve 81c^2v^2-49d^4u^4

$$81 c ^ { 2 } v ^ { 2 } - 49 d ^ { 4 } u ^ { 4 }$$

Factor

$$\left(9cv-7d^{2}u^{2}\right)\left(7d^{2}u^{2}+9cv\right)$$

Solution Steps

Rewrite 81c^{2}v^{2}-49d^{4}u^{4} as \left(9cv\right)^{2}-\left(7d^{2}u^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9cv-7d^{2}u^{2}\right)\left(9cv+7d^{2}u^{2}\right)$$

Reorder the terms.

$$\left(-7d^{2}u^{2}+9cv\right)\left(7d^{2}u^{2}+9cv\right)$$

Evaluate

$$81\left(cv\right)^{2}-49\left(du\right)^{4}$$