Factor
\frac{\left(3n-1\right)\left(9n^{2}+3n+1\right)}{27}
Evaluate
n^{3}-\frac{1}{27}
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\frac{27n^{3}-1}{27}
Factor out \frac{1}{27}.
\left(3n-1\right)\left(9n^{2}+3n+1\right)
Consider 27n^{3}-1. Rewrite 27n^{3}-1 as \left(3n\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).
\frac{\left(3n-1\right)\left(9n^{2}+3n+1\right)}{27}
Rewrite the complete factored expression. Polynomial 9n^{2}+3n+1 is not factored since it does not have any rational roots.
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