Solve 9x^4-9x

$$9 x ^ { 4 } - 9 x$$

Factor

$$9x\left(x-1\right)\left(x^{2}+x+1\right)$$

Solution Steps

Factor out 9.

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

Consider x^{4}-x. Factor out x.

$$x\left(x^{3}-1\right)$$

Consider x^{3}-1. Rewrite x^{3}-1 as x^{3}-1^{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).

$$\left(x-1\right)\left(x^{2}+x+1\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+x+1 is not factored since it does not have any rational roots.

$$9x\left(x-1\right)\left(x^{2}+x+1\right)$$

Evaluate

$$9x\left(x^{3}-1\right)$$