Factor
3\left(3x-1\right)\left(9x^{2}+3x+1\right)
Evaluate
81x^{3}-3
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3\left(27x^{3}-1\right)
Factor out 3.
\left(3x-1\right)\left(9x^{2}+3x+1\right)
Consider 27x^{3}-1. Rewrite 27x^{3}-1 as \left(3x\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).
3\left(3x-1\right)\left(9x^{2}+3x+1\right)
Rewrite the complete factored expression. Polynomial 9x^{2}+3x+1 is not factored since it does not have any rational roots.
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