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4MA1/1HR Jan 2021, Question 16: Expand and Simplify

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks

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The question, in short

Expand and simplify a product of three binomials, then rewrite a quadratic in completed-square form with integer a and b.

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

Part (a) · 3 marks

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

  1. 1(x + 4)(x − 2) = x² − 2x + 4x − 8 = x² + 2x − 8
  2. 2(x² + 2x − 8)(x + 1) = x³ + x² + 2x² + 2x − 8x − 8
  3. 3Collect like terms: x³ + 3x² − 6x − 8

Answerx³ + 3x² − 6x − 8

Part (b) · 2 marks

Write x² − 10x + 40 as (x + a)² + b, with a and b integers.

  1. 1Halve −10 to get −5: (x − 5)² = x² − 10x + 25
  2. 2So x² − 10x + 40 = (x − 5)² − 25 + 40
  3. 3−25 + 40 = 15, so the answer is (x − 5)² + 15

Answer(x − 5)² + 15

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