Evaluate
\frac{x^{3}}{3}-\frac{x^{2}}{2}+\frac{27x}{8}+\frac{189}{64}
Expand
\frac{x^{3}}{3}-\frac{x^{2}}{2}+\frac{27x}{8}+\frac{189}{64}
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\frac{8}{27}x^{3}-x^{2}+\frac{9}{8}x-\frac{27}{64}+\left(\frac{1}{3}x+\frac{3}{2}\right)^{3}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(\frac{2}{3}x-\frac{3}{4}\right)^{3}.
\frac{8}{27}x^{3}-x^{2}+\frac{9}{8}x-\frac{27}{64}+\frac{1}{27}x^{3}+\frac{1}{2}x^{2}+\frac{9}{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(\frac{1}{3}x+\frac{3}{2}\right)^{3}.
\frac{1}{3}x^{3}-x^{2}+\frac{9}{8}x-\frac{27}{64}+\frac{1}{2}x^{2}+\frac{9}{4}x+\frac{27}{8}
Combine \frac{8}{27}x^{3} and \frac{1}{27}x^{3} to get \frac{1}{3}x^{3}.
\frac{1}{3}x^{3}-\frac{1}{2}x^{2}+\frac{9}{8}x-\frac{27}{64}+\frac{9}{4}x+\frac{27}{8}
Combine -x^{2} and \frac{1}{2}x^{2} to get -\frac{1}{2}x^{2}.
\frac{1}{3}x^{3}-\frac{1}{2}x^{2}+\frac{27}{8}x-\frac{27}{64}+\frac{27}{8}
Combine \frac{9}{8}x and \frac{9}{4}x to get \frac{27}{8}x.
\frac{1}{3}x^{3}-\frac{1}{2}x^{2}+\frac{27}{8}x+\frac{189}{64}
Add -\frac{27}{64} and \frac{27}{8} to get \frac{189}{64}.
\frac{8}{27}x^{3}-x^{2}+\frac{9}{8}x-\frac{27}{64}+\left(\frac{1}{3}x+\frac{3}{2}\right)^{3}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(\frac{2}{3}x-\frac{3}{4}\right)^{3}.
\frac{8}{27}x^{3}-x^{2}+\frac{9}{8}x-\frac{27}{64}+\frac{1}{27}x^{3}+\frac{1}{2}x^{2}+\frac{9}{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(\frac{1}{3}x+\frac{3}{2}\right)^{3}.
\frac{1}{3}x^{3}-x^{2}+\frac{9}{8}x-\frac{27}{64}+\frac{1}{2}x^{2}+\frac{9}{4}x+\frac{27}{8}
Combine \frac{8}{27}x^{3} and \frac{1}{27}x^{3} to get \frac{1}{3}x^{3}.
\frac{1}{3}x^{3}-\frac{1}{2}x^{2}+\frac{9}{8}x-\frac{27}{64}+\frac{9}{4}x+\frac{27}{8}
Combine -x^{2} and \frac{1}{2}x^{2} to get -\frac{1}{2}x^{2}.
\frac{1}{3}x^{3}-\frac{1}{2}x^{2}+\frac{27}{8}x-\frac{27}{64}+\frac{27}{8}
Combine \frac{9}{8}x and \frac{9}{4}x to get \frac{27}{8}x.
\frac{1}{3}x^{3}-\frac{1}{2}x^{2}+\frac{27}{8}x+\frac{189}{64}
Add -\frac{27}{64} and \frac{27}{8} to get \frac{189}{64}.
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