0606/22 Oct/Nov 2025, Question 3: The Binomial Expansion
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 6 marks
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The question, in short
Determine the exact constant term, free of x, in the product of the binomial expansions (2 + 3/x²)¹⁰ and (1 − 4x²)².
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Solution · 6 marks
- 1(2 + 3/x²)¹⁰ = 2¹⁰ + 10 × 2⁹ × (3/x²) + 45 × 2⁸ × (3/x²)² + …
- 2= 1024 + 15 360/x² + 103 680/x⁴ + …
- 3(1 − 4x²)² = 1 − 8x² + 16x⁴
- 4Term independent of x = 1024 × 1 + 15 360 × (−8) + 103 680 × 16
- 5= 1024 − 122 880 + 1 658 880 = 1 537 024
Answer1 537 024
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Also searched as: 0606/22/O/N/25 · 0606_w25_qp_22 · 0606 w25 22 · question 3.
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