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4MA1/2HR Jan 2023, Question 12: Further Expansion

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks

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The question, in short

Simplify three algebraic expressions: a power with a zero index, a fractional power of a product, and a product of three factors.

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

Part (a) · 1 mark

Simplify 2 divided by y⁰.

  1. 1y⁰ = 1 for any non-zero y
  2. 2So 2/y⁰ = 2 ÷ 1 = 2

Answer2

Part (b) · 2 marks

Simplify fully (16a⁴)^(3/4).

  1. 1(16a⁴)^(3/4) = 16^(3/4) × (a⁴)^(3/4)
  2. 216^(3/4) = (⁴√16)³ = 2³ = 8
  3. 3(a⁴)^(3/4) = a^(4 × 3/4) = a³
  4. 4So (16a⁴)^(3/4) = 8a³

Answer8a³

Part (c) · 3 marks

Expand and simplify 5x(3x + 4)(2x − 1).

  1. 1Expand the brackets: (3x + 4)(2x − 1) = 6x² − 3x + 8x − 4 = 6x² + 5x − 4
  2. 2Multiply each term by 5x: 5x × 6x² + 5x × 5x − 5x × 4
  3. 3= 30x³ + 25x² − 20x

Answer30x³ + 25x² − 20x

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