Evaluate
\frac{27\left(18x-1\right)^{3}}{8}
Expand
19683x^{3}-\frac{6561x^{2}}{2}+\frac{729x}{4}-\frac{27}{8}
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19683x^{3}-\frac{6561}{2}x^{2}+\frac{729}{4}x-\frac{27}{8}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(27x-\frac{3}{2}\right)^{3}.
19683x^{3}-\frac{6561}{2}x^{2}+\frac{729}{4}x-\frac{27}{8}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(27x-\frac{3}{2}\right)^{3}.
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