Expand the binomial expression (X - ½X)⁵

Answer 1

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:

\[ \frac{1}{32}X^5 \]