Solve 27r^3+1/27

$$27 r ^ { 3 } + \frac { 1 } { 27 }$$

Factor

$$\frac{\left(9r+1\right)\left(81r^{2}-9r+1\right)}{27}$$

Solution Steps

Factor out \frac{1}{27}.

$$\frac{729r^{3}+1}{27}$$

Consider 729r^{3}+1. Rewrite 729r^{3}+1 as \left(9r\right)^{3}+1^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(9r+1\right)\left(81r^{2}-9r+1\right)$$

Rewrite the complete factored expression. Polynomial 81r^{2}-9r+1 is not factored since it does not have any rational roots.

$$\frac{\left(9r+1\right)\left(81r^{2}-9r+1\right)}{27}$$

Evaluate

$$27r^{3}+\frac{1}{27}$$