Solve 5s^4-405

$$5 s ^ { 4 } - 405$$

Factor

$$5\left(s-3\right)\left(s+3\right)\left(s^{2}+9\right)$$

Solution Steps

Factor out 5.

$$5\left(s^{4}-81\right)$$

Consider s^{4}-81. Rewrite s^{4}-81 as \left(s^{2}\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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

$$\left(s-3\right)\left(s+3\right)$$

Rewrite the complete factored expression. Polynomial s^{2}+9 is not factored since it does not have any rational roots.

$$5\left(s-3\right)\left(s+3\right)\left(s^{2}+9\right)$$

Evaluate

$$5\left(s^{4}-81\right)$$