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0606/23 May/Jun 2026, Question 3: The Binomial Expansion

Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 5 marks

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The question, in short

Multiply out the product of the two brackets, then use that result to get the x⁵ coefficient in the product of the tenth and twelfth powers.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Write the product of the two linear brackets as a simplified polynomial.

  1. 1(1 + 2x)(1 − 2x) = 1 − 2x + 2x − 4x² = 1 − 4x²

Answer1 − 4x²

Part (b) · 4 marks

Using part a, determine the number multiplying x⁵ in the expansion of the two high powers.

  1. 1(1 + 2x)¹⁰(1 − 2x)¹² = (1 − 4x²)¹⁰(1 − 2x)²
  2. 2(1 − 2x)² = 1 − 4x + 4x²
  3. 3(1 − 4x²)¹⁰ has only even powers; x⁴ term: ¹⁰C₂(−4x²)² = 45 × 16x⁴ = 720x⁴
  4. 4x⁵ term only from (−4x) × 720x⁴
  5. 5Coefficient = −2880

Answer−2880

Stuck on a step? Read the free lesson: The Binomial Expansion

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Also searched as: 0606/23/M/J/26 · 0606_s26_qp_23 · 0606 s26 23 · question 3.
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