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WMA12/01 Jan 2020, Question 2: The Binomial Expansion

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

The question, in short

Given that a term of the binomial expansion of (3 + ax)⁶ is 540x⁴, find the constant a and then a term independent of x in a related product.

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

Part (a) · 4 marks

Use the general term of the expansion of (3 + ax)⁶ to form an equation from the x⁴ coefficient equal to 540, then solve for the possible values of a.

  1. 1The x⁴ term is ⁶C₄ × 3² × (ax)⁴ = 135a⁴x⁴
  2. 2135a⁴ = 540
  3. 3a⁴ = 4
  4. 4a = ±√2

Answera = ±√2

Part (b) · 3 marks

Using the value of a found, expand the product (1/81 + 1/x⁶)(3 + ax)⁶ and identify the term containing no x.

  1. 1Constant from 1/81 × (constant term of (3 + ax)⁶) = 1/81 × 3⁶ = 9
  2. 2Constant from 1/x⁶ × (x⁶ term) = a⁶ = (±√2)⁶ = 8
  3. 3Term independent of x = 9 + 8
  4. 4= 17

Answer17

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