Solve 81v^4-900v^2

$$81 v ^ { 4 } - 900 v ^ { 2 }$$

Factor

$$9\left(3v-10\right)\left(3v+10\right)v^{2}$$

Solution Steps

Factor out 9.

$$9\left(9v^{4}-100v^{2}\right)$$

Consider 9v^{4}-100v^{2}. Factor out v^{2}.

$$v^{2}\left(9v^{2}-100\right)$$

Consider 9v^{2}-100. Rewrite 9v^{2}-100 as \left(3v\right)^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3v-10\right)\left(3v+10\right)$$

Rewrite the complete factored expression.

$$9v^{2}\left(3v-10\right)\left(3v+10\right)$$

Evaluate

$$81v^{4}-900v^{2}$$