To expand the binomial expression \((X - \frac{1}{2}X)^5\), we first simplify the expression inside the parentheses.
\[ X - \frac{1}{2}X = \frac{1}{2}X \]
So, we need to expand:
\[ \left(\frac{1}{2}X\right)^5 \]
Using the binomial theorem, or simply raising the term to the fifth power:
\[ \left(\frac{1}{2}X\right)^5 = \left(\frac{1}{2}\right)^5 \cdot X^5 = \frac{1}{32} \cdot X^5 \]
Thus, the expansion of the expression \((X - \frac{1}{2}X)^5\) is:
\[ \frac{1}{32}X^5 \]
So, the final result is:
\[ \frac{1}{32}X^5 \]
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