Question:
The coefficient of \(x^3\) in the expansion of
\[
\left(x - \frac{1}{x}\right)^7
\]
is:
The coefficient of \(x^3\) in the expansion of
\[ \left(x - \frac{1}{x}\right)^7 \]
is:
\[ \left(x - \frac{1}{x}\right)^7 \]
is:
Show Hint
Match the power of x to find the required term.
Updated On: Mar 23, 2026
- 14
- 21
- 28
- 35
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: General term:
\[ T_{k+1} = \binom{7}{k} x^{7-2k} (-1)^k \]
Step 2: Set power \(7 - 2k = 3 \implies k = 2\).
Step 3: Coefficient:
\[ \binom{7}{2} = 21 \]
\[ T_{k+1} = \binom{7}{k} x^{7-2k} (-1)^k \]
Step 2: Set power \(7 - 2k = 3 \implies k = 2\).
Step 3: Coefficient:
\[ \binom{7}{2} = 21 \]
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