Solve 75u^2v^2-3v^4

$$75 u ^ { 2 } v ^ { 2 } - 3 v ^ { 4 }$$

Factor

$$3\left(5u-v\right)\left(5u+v\right)v^{2}$$

Solution Steps

Factor out 3.

$$3\left(25u^{2}v^{2}-v^{4}\right)$$

Consider 25u^{2}v^{2}-v^{4}. Factor out v^{2}.

$$v^{2}\left(25u^{2}-v^{2}\right)$$

Consider 25u^{2}-v^{2}. Rewrite 25u^{2}-v^{2} as \left(5u\right)^{2}-v^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5u-v\right)\left(5u+v\right)$$

Rewrite the complete factored expression.

$$3v^{2}\left(5u-v\right)\left(5u+v\right)$$

Evaluate

$$75\left(uv\right)^{2}-3v^{4}$$