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4MA1/1HR Jun 2024, Question 14: 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 linear factors, then simplify a fractional expression with negative indices raised to a negative power.

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)(2 − x)(4 + x).

  1. 1(3x + 1)(2 − x) = 6x − 3x² + 2 − x = −3x² + 5x + 2
  2. 2(−3x² + 5x + 2)(4 + x) = −12x² − 3x³ + 20x + 5x² + 8 + 2x
  3. 3−3x³ + (−12x² + 5x²) + (20x + 2x) + 8
  4. 4−3x³ − 7x² + 22x + 8

Answer−3x³ − 7x² + 22x + 8

Part (b) · 3 marks

Simplify fully (a³b/(a⁹b⁵))^(−1/2).

  1. 1(a³b/(a⁹b⁵))^(−1/2) = (a^(3 − 9) b^(1 − 5))^(−1/2) = (a⁻⁶b⁻⁴)^(−1/2)
  2. 2= a^((−6) × (−1/2)) b^((−4) × (−1/2))
  3. 3= a³b²

Answera³b²

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