Solve r^4-r

$$r ^ { 4 } - r$$

Factor

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

Solution Steps

Factor out r.

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

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

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

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

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

Evaluate

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