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0580/21 May/Jun 2024, Question 19: Difference of Two Squares

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 5 marks

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The question, in short

Factorise two algebraic expressions completely: a difference of two squares with coefficients 12 and 75, and a four-term expression by grouping.

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

Part (a) · 3 marks

Factorise 12m² − 75t² fully, taking out the common factor first then using a difference of two squares.

  1. 112m² − 75t² = 3(4m² − 25t²)
  2. 24m² − 25t² = (2m)² − (5t)² is a difference of two squares
  3. 3= 3(2m + 5t)(2m − 5t)

Answer3(2m + 5t)(2m − 5t)

Part (b) · 2 marks

Factorise xy + 15 + 3y + 5x completely by grouping the terms into pairs.

  1. 1xy + 5x + 3y + 15
  2. 2= x(y + 5) + 3(y + 5)
  3. 3= (x + 3)(y + 5)

Answer(x + 3)(y + 5)

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Also searched as: 0580/21/M/J/24 · 0580_s24_qp_21 · 0580 s24 21 · question 19.
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