Factor
\frac{\left(5v-1\right)\left(25v^{2}+5v+1\right)}{125}
Evaluate
v^{3}-\frac{1}{125}
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\frac{125v^{3}-1}{125}
Factor out \frac{1}{125}.
\left(5v-1\right)\left(25v^{2}+5v+1\right)
Consider 125v^{3}-1. Rewrite 125v^{3}-1 as \left(5v\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(5v-1\right)\left(25v^{2}+5v+1\right)}{125}
Rewrite the complete factored expression. Polynomial 25v^{2}+5v+1 is not factored since it does not have any rational roots.
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