Solve 9v^4-36v^2

$$9 v ^ { 4 } - 36 v ^ { 2 }$$

Factor

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

Solution Steps

Factor out 9.

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

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

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

Consider v^{2}-4. Rewrite v^{2}-4 as v^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-2\right)\left(v+2\right)$$

Rewrite the complete factored expression.

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

Evaluate

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