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4MA1/2H Jun 2022, Question 14: Rearranging Formulas

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

Expand and simplify the product of three brackets (5 − x)(2x + 3)(x + 4), showing working, then rearrange g = (c + 3)/(4 + c) − 7 to make c the subject.

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Part (a) · 3 marks

Expand and simplify (5 − x)(2x + 3)(x + 4), showing clear working.

  1. 1Multiply two brackets first: (5 − x)(2x + 3) = 10x + 15 − 2x² − 3x
  2. 2Simplify: −2x² + 7x + 15
  3. 3Multiply by (x + 4): −2x³ − 8x² + 7x² + 28x + 15x + 60
  4. 4Collect like terms: −2x³ − x² + 43x + 60

Answer−2x³ − x² + 43x + 60

Part (b) · 4 marks

Rearrange g = (c + 3)/(4 + c) − 7 to make c the subject.

  1. 1Add 7: g + 7 = (c + 3)/(4 + c)
  2. 2Multiply out: (g + 7)(4 + c) = c + 3, so 4g + gc + 28 + 7c = c + 3
  3. 3Collect c terms: gc + 6c = −4g − 25
  4. 4Factorise: c(g + 6) = −4g − 25
  5. 5c = (25 + 4g)/(−6 − g)

Answerc = (25 + 4g)/(−6 − g)

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