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WMA12/01 Jan 2025, Question 2: The Binomial Expansion

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 5 marks

The question, in short

Expand (2 − 5x)⁸ up to the x³ term in increasing powers, simplifying each coefficient, then choose the x value that would approximate 2.05⁸.

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Part (a) · 4 marks

Write the first four terms of the expansion of (2 − 5x)⁸ in ascending powers of x, with every term fully simplified.

  1. 1(2 − 5x)⁸ = 2⁸ + ⁸C₁(2)⁷(−5x) + ⁸C₂(2)⁶(−5x)² + ⁸C₃(2)⁵(−5x)³ + …
  2. 22⁸ = 256
  3. 38 × 128 × (−5x) = −5120x
  4. 428 × 64 × 25x² = 44800x²
  5. 556 × 32 × (−125x³) = −224000x³

Answer256 − 5120x + 44800x² − 224000x³

Part (b) · 1 mark

Give the number to substitute for x so the expansion estimates 2.05⁸; no evaluation needed.

  1. 12 − 5x = 2.05
  2. 25x = −0.05
  3. 3x = −0.01

Answerx = −0.01

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