Factor
\frac{\left(5a-1\right)\left(25a^{2}+5a+1\right)}{125}
Evaluate
a^{3}-\frac{1}{125}
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\frac{125a^{3}-1}{125}
Factor out \frac{1}{125}.
\left(5a-1\right)\left(25a^{2}+5a+1\right)
Consider 125a^{3}-1. Rewrite 125a^{3}-1 as \left(5a\right)^{3}-1^{3}. The difference of cubes can be factored using the rule: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).
\frac{\left(5a-1\right)\left(25a^{2}+5a+1\right)}{125}
Rewrite the complete factored expression. Polynomial 25a^{2}+5a+1 is not factored since it does not have any rational roots.
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