Factor
2\left(3w+1\right)\left(9w^{2}-3w+1\right)
Evaluate
54w^{3}+2
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2\left(27w^{3}+1\right)
Factor out 2.
\left(3w+1\right)\left(9w^{2}-3w+1\right)
Consider 27w^{3}+1. Rewrite 27w^{3}+1 as \left(3w\right)^{3}+1^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).
2\left(3w+1\right)\left(9w^{2}-3w+1\right)
Rewrite the complete factored expression. Polynomial 9w^{2}-3w+1 is not factored since it does not have any rational roots.
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