0606/21 Oct/Nov 2025, Question 10: The Binomial Expansion
Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 5 marks
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The question, in short
Given the first three ascending-power terms 640 + b²x + 30240x² of 5(2 + ax)ⁿ, find a and the possible values of b.
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Solution · 5 marks
- 1Constant term: 5 × 2ⁿ = 640, so 2ⁿ = 128 and n = 7
- 2x² term: 5 × (7 × 6/2) × 2⁵ × a² = 30 240
- 33360a² = 30 240, so a² = 9
- 4x term: 5 × 7 × 2⁶ × a = b², so b² = 2240a
- 5b² must be positive, so a = 3 only
- 6b² = 6720, b = ±√6720 = ±8√105
Answera = 3, b = ±√6720 (= ±8√105)
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Also searched as: 0606/21/O/N/25 · 0606_w25_qp_21 · 0606 w25 21 · question 10.
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