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4MA1/1HR Jun 2022, Question 16: Expand and Simplify

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks

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The question, in short

Expand and simplify the product of three brackets, then simplify a negative-index algebraic fraction.

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

Part (a) · 3 marks

Expand and simplify (3x − 1)(x + 2)(3x + 1).

  1. 1Difference of two squares: (3x − 1)(3x + 1) = 9x² − 1
  2. 2Multiply by (x + 2): 9x²(x + 2) − 1(x + 2)
  3. 3= 9x³ + 18x² − x − 2

Answer9x³ + 18x² − x − 2

Part (b) · 3 marks

Simplify fully (2x⁵ ÷ (8xy²))⁻², giving the result in its simplest form.

  1. 1Simplify inside first: 2x⁵/(8xy²) = x⁴/(4y²)
  2. 2A power of −2 means flip, then square: (4y²/x⁴)²
  3. 3= 16y⁴/x⁸

Answer16y⁴/x⁸

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