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0580/12 Feb/Mar 2022, Question 23: Expanding Two Brackets

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 4 marks

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The question, in short

Expand and simplify (x + 3)(x − 5), then explain why 2x(4x − 6) is not a complete factorisation of 8x² − 12x and give the fully factorised form.

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Part (a) · 2 marks

Multiply out the two brackets (x + 3)(x − 5) and collect like terms to give a simplified expression.

  1. 1(x + 3)(x − 5) = x² − 5x + 3x − 15
  2. 2= x² − 2x − 15

Answerx² − 2x − 15

Part (b) · 2 marks

State why 2x(4x − 6) fails to score full marks and write the correct complete factorisation of 8x² − 12x.

  1. 14x − 6 still has a common factor of 2, so it is not factorised completely
  2. 2Highest common factor of 8x² and 12x is 4x
  3. 38x² − 12x = 4x(2x − 3)

AnswerCorrect reason; 4x(2x − 3)

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Also searched as: 0580/12/F/M/22 · 0580_m22_qp_12 · 0580 m22 12 · question 23.
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