Solve 27s^4-64s

$$27 s ^ { 4 } - 64 s$$

Factor

$$s\left(3s-4\right)\left(9s^{2}+12s+16\right)$$

Solution Steps

Factor out s.

$$s\left(27s^{3}-64\right)$$

Consider 27s^{3}-64. Rewrite 27s^{3}-64 as \left(3s\right)^{3}-4^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(3s-4\right)\left(9s^{2}+12s+16\right)$$

Rewrite the complete factored expression. Polynomial 9s^{2}+12s+16 is not factored since it does not have any rational roots.

$$s\left(3s-4\right)\left(9s^{2}+12s+16\right)$$

Evaluate

$$s\left(27s^{3}-64\right)$$