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4MA1/2HR Jun 2025, Question 13: Further Expansion

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks

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The question, in short

Factorise a difference of two squares in x and y, then expand a product of three factors into a cubic and identify the integer coefficients.

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

Part (a) · 2 marks

Factorise 4x² − 25y².

  1. 14x² = (2x)² and 25y² = (5y)²
  2. 2Difference of two squares: (2x)² − (5y)²
  3. 3= (2x + 5y)(2x − 5y)

Answer(2x + 5y)(2x − 5y)

Part (b) · 3 marks

Expand 4x(x + 3)(2x − 5) into the form ax³ + bx² + cx and find integers a, b, c.

  1. 1(x + 3)(2x − 5) = 2x² − 5x + 6x − 15
  2. 2= 2x² + x − 15
  3. 34x(2x² + x − 15) = 8x³ + 4x² − 60x
  4. 4a = 8, b = 4, c = −60

Answer8x³ + 4x² − 60x

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