Solve 8x^3-1/27

$$8 x ^ { 3 } - \frac { 1 } { 27 }$$

Factor

$$\frac{\left(6x-1\right)\left(36x^{2}+6x+1\right)}{27}$$

Solution Steps

Factor out \frac{1}{27}.

$$\frac{216x^{3}-1}{27}$$

Consider 216x^{3}-1. Rewrite 216x^{3}-1 as \left(6x\right)^{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).

$$\left(6x-1\right)\left(36x^{2}+6x+1\right)$$

Rewrite the complete factored expression. Polynomial 36x^{2}+6x+1 is not factored since it does not have any rational roots.

$$\frac{\left(6x-1\right)\left(36x^{2}+6x+1\right)}{27}$$

Evaluate

$$8x^{3}-\frac{1}{27}$$