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WMA12/01 Jun 2023, Question 4: The Binomial Expansion

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Expand (3 + px)⁵ in ascending powers of x up to the x³ term, then use the given condition linking B and D with p < 0 to find constants.

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

Part (a) · 1 mark

Find the constant term A of the expansion of (3 + px)⁵.

  1. 1Constant term = 3⁵
  2. 2A = 243

AnswerA = 243

Part (bi) · 4 marks

Given B = 18D and p < 0, find the value of the constant p.

  1. 1B = 5 × 3⁴ × p = 405p
  2. 2D = 10 × 3² × p³ = 90p³
  3. 3B = 18D: 405p = 1620p³
  4. 4Divide by p (p ≠ 0): p² = 405/1620 = 1/4
  5. 5p < 0, so p = −½

Answerp = −½

Part (bii) · 2 marks

Using the found value of p, find the coefficient C of x².

  1. 1C = ⁵C₂ × 3³ × p² = 10 × 27 × p² = 270p²
  2. 2p² = 1/4, so C = 270/4
  3. 3C = 135/2 = 67.5

AnswerC = 135/2 (= 67.5)

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

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Also searched as: WMA12 June 2023 · WMA12/01 · wma12 jun23 · IAS Maths Pure Mathematics 2 June 2023 · question 4.
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