Find the coefficient of x³ in the binomial expansion of (x + 2)⁵.
Answer and explanation
Correct answer: B. 40
- Step 1: General term in (x + a)ⁿ is T_(r+1) = (n choose r) x^(n-r) a^r. Step 2. For x³, n - r = 3 => 5 - r = 3 => r = 2. Step 3. Coefficient = (5 choose 2) × 2² = 10 × 4 = 40. Answer: 40. Why not the others: 10 is (5 choose 2) without 2²; 20 uses 2¹; 80 uses 2³.
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