Evaluate
\left(2x-3\right)^{3}+\frac{x}{2}-\frac{1}{2}
Expand
8x^{3}-36x^{2}+\frac{109x}{2}-\frac{55}{2}
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8x^{3}-36x^{2}+54x-27+\frac{1}{2}\left(x-1\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x-3\right)^{3}.
8x^{3}-36x^{2}+54x-27+\frac{1}{2}x-\frac{1}{2}
Use the distributive property to multiply \frac{1}{2} by x-1.
8x^{3}-36x^{2}+\frac{109}{2}x-27-\frac{1}{2}
Combine 54x and \frac{1}{2}x to get \frac{109}{2}x.
8x^{3}-36x^{2}+\frac{109}{2}x-\frac{55}{2}
Subtract \frac{1}{2} from -27 to get -\frac{55}{2}.
8x^{3}-36x^{2}+54x-27+\frac{1}{2}\left(x-1\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x-3\right)^{3}.
8x^{3}-36x^{2}+54x-27+\frac{1}{2}x-\frac{1}{2}
Use the distributive property to multiply \frac{1}{2} by x-1.
8x^{3}-36x^{2}+\frac{109}{2}x-27-\frac{1}{2}
Combine 54x and \frac{1}{2}x to get \frac{109}{2}x.
8x^{3}-36x^{2}+\frac{109}{2}x-\frac{55}{2}
Subtract \frac{1}{2} from -27 to get -\frac{55}{2}.
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