Solve 45u^4-20u^2

$$45 u ^ { 4 } - 20 u ^ { 2 }$$

Factor

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

Solution Steps

Factor out 5.

$$5\left(9u^{4}-4u^{2}\right)$$

Consider 9u^{4}-4u^{2}. Factor out u^{2}.

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

Consider 9u^{2}-4. Rewrite 9u^{2}-4 as \left(3u\right)^{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).

$$\left(3u-2\right)\left(3u+2\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$45u^{4}-20u^{2}$$