Example 1 · level 1
Find the coefficient of x² in the expansion of (1 + x)⁶.
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- 6C2 = 15.
Answer: 15
CLASS 11 MATHS · BINOMIAL THEOREM
Binomial theorem: coefficients and special terms
The general term of (a + b)ⁿ is Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ. Match the power of x to find r, then compute the coefficient.
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Worked examples
Example 2 · level 2
Find the coefficient of x¹ in the expansion of (2x + 3)⁵.
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- Term with x¹: 5C1 × 2¹ × 3⁴ × x¹.
- Coefficient = 5 × 2 × 81 = 810.
Answer: 810
Example 3 · level 3
Find the coefficient of the middle term in the expansion of (x − 2)⁸.
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- Middle term is T5 (r = 4).
- Coefficient = 70 × (−2)⁴ = 1,120.
Answer: 1,120