Question:
Coefficient of \( x \) in \( (1 - 3x + 7x^2)(1 - x)^{16} \)
Coefficient of \( x \) in \( (1 - 3x + 7x^2)(1 - x)^{16} \)
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Focus only on terms that contribute to required power.
Updated On: May 1, 2026
- \( 17 \)
- \( 19 \)
- \( -17 \)
- \( -19 \)
- \( 20 \)
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The Correct Option is D
Solution and Explanation
Concept: Collect coefficient of \( x \).
Step 1: Expand relevant terms.
\[ (1 - 3x + 7x^2)(1 - 16x + \cdots) \]
Step 2: Only terms contributing to \( x \).
\[ 1(-16x), (-3x)(1) \]
Step 3: Multiply.
\[ -16x -3x \]
Step 4: Add contributions.
\[ -19x \]
Step 5: Coefficient: \[ -19 \]
Step 1: Expand relevant terms.
\[ (1 - 3x + 7x^2)(1 - 16x + \cdots) \]
Step 2: Only terms contributing to \( x \).
\[ 1(-16x), (-3x)(1) \]
Step 3: Multiply.
\[ -16x -3x \]
Step 4: Add contributions.
\[ -19x \]
Step 5: Coefficient: \[ -19 \]
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