Factor
\frac{\left(2r-1\right)\left(4r^{2}+2r+1\right)}{8}
Evaluate
r^{3}-\frac{1}{8}
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\frac{8r^{3}-1}{8}
Factor out \frac{1}{8}.
\left(2r-1\right)\left(4r^{2}+2r+1\right)
Consider 8r^{3}-1. Rewrite 8r^{3}-1 as \left(2r\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(2r-1\right)\left(4r^{2}+2r+1\right)}{8}
Rewrite the complete factored expression. Polynomial 4r^{2}+2r+1 is not factored since it does not have any rational roots.
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