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x^{3}-\frac{3}{2}x^{2}+\frac{3}{4}x-\frac{1}{8}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-\frac{1}{2}\right)^{3}.
x^{3}-\frac{3}{2}x^{2}+\frac{3}{4}x-\frac{1}{8}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-\frac{1}{2}\right)^{3}.