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4MA1/2H Nov 2021, Question 12: Further Expansion

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

Three algebra tasks: simplify a power of a product, combine three algebraic fractions into one, and expand and simplify a product of three factors.

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

Part (a) · 2 marks

Simplify (64p⁹q¹²)^(2/3), giving the result in its simplest form.

  1. 164^(2/3) = (∛64)² = 4² = 16
  2. 2(p⁹)^(2/3) = p⁶ and (q¹²)^(2/3) = q⁸
  3. 3= 16p⁶q⁸

Answer16p⁶q⁸

Part (b) · 2 marks

Write 2/(3x) + 4/(5x) − 9/(10x) as a single fraction in simplest form.

  1. 1Common denominator 30x
  2. 22/(3x) = 20/(30x), 4/(5x) = 24/(30x), 9/(10x) = 27/(30x)
  3. 3(20 + 24 − 27)/(30x) = 17/(30x)

Answer17/(30x)

Part (c) · 3 marks

Expand and simplify 4x(x − 5)(2x + 3), showing working clearly.

  1. 1(x − 5)(2x + 3) = 2x² + 3x − 10x − 15 = 2x² − 7x − 15
  2. 24x(2x² − 7x − 15)
  3. 3= 8x³ − 28x² − 60x

Answer8x³ − 28x² − 60x

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