0606/22 Feb/Mar 2025, Question 10: The Binomial Expansion
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 10 marks
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The question, in short
Given the first three terms 81x⁴ + 999x³ + cx² of the descending expansion of (ax − 2)⁴(1 + b/x)³, find positive integers a, b and c.
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Solution · 10 marks
- 1(ax − 2)⁴ = a⁴x⁴ − 8a³x³ + 24a²x² − …
- 2(1 + b/x)³ = 1 + 3b/x + 3b²/x² + …
- 3x⁴: a⁴ = 81, so a = 3
- 4x³: 3a⁴b − 8a³ = 999, so 243b − 216 = 999, b = 5
- 5x²: c = 3a⁴b² − 24a³b + 24a² = 6075 − 3240 + 216 = 3051
Answera = 3, b = 5, c = 3051
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Also searched as: 0606/22/F/M/25 · 0606_m25_qp_22 · 0606 m25 22 · question 10.
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