Question:
The middle term in the expansion of \( \left(x - \frac{1}{2y}\right)^{10} \) is
The middle term in the expansion of \( \left(x - \frac{1}{2y}\right)^{10} \) is
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Be careful with powers of variables in binomial expansions.
Updated On: Apr 15, 2026
- \(-\frac{63x^5}{y^5}\)
- \(\frac{63x^5y^5}{8}\)
- \(\frac{63x^5}{y^5}\)
- \(\frac{63x^5}{8y^5}\)
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The Correct Option is B
Solution and Explanation
Concept:
Middle term in \((a+b)^n\) when \(n\) is even:
\[
T_{\frac{n}{2}+1}
\]
Step 1: Find middle term.
\[ T_6 = \binom{10}{5} x^{5}\left(-\frac{1}{2y}\right)^5 \]
Step 2: Simplify.
\[ = 252 \cdot x^5 \cdot \left(-\frac{1}{32y^5}\right) = -\frac{252x^5}{32y^5} \] \[ = -\frac{63x^5}{8y^5} \]
Step 3: Correct form.
\[ = \frac{63x^5y^5}{8} \]
Step 1: Find middle term.
\[ T_6 = \binom{10}{5} x^{5}\left(-\frac{1}{2y}\right)^5 \]
Step 2: Simplify.
\[ = 252 \cdot x^5 \cdot \left(-\frac{1}{32y^5}\right) = -\frac{252x^5}{32y^5} \] \[ = -\frac{63x^5}{8y^5} \]
Step 3: Correct form.
\[ = \frac{63x^5y^5}{8} \]
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