0606/22 May/Jun 2026, Question 6: The Binomial Expansion
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 8 marks
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The question, in short
Expand (a + x)⁴(1 + ax)⁵ in ascending powers of x, match the first three terms to 16 + bx + cx², and find all possible integer values of a, b and c.
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Solution · 8 marks
- 1(a + x)⁴ = a⁴ + 4a³x + 6a²x² + …
- 2(1 + ax)⁵ = 1 + 5ax + 10a²x² + …
- 3Constant: a⁴ = 16, so a = ±2
- 4b = 5a⁵ + 4a³: a = 2 gives b = 160 + 32 = 192; a = −2 gives b = −192
- 5c = 10a⁶ + 20a⁴ + 6a² = 640 + 320 + 24 = 984 for both
Answera = 2, b = 192, c = 984 or a = −2, b = −192, c = 984
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Also searched as: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 6.
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