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0580/13 Oct/Nov 2025, Question 17: Expanding Two Brackets

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Non-calculator · 5 marks

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The question, in short

Three short algebra tasks: find an unknown index in a product of powers of k, expand and simplify a product of two binomials, and factorise a two-term expression in r.

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

Part (a) · 1 mark

Given k raised to x times k to the 5 equals k to the 20, find the value of x.

  1. 1kˣ × k⁵ = kˣ⁺⁵, so x + 5 = 20
  2. 2x = 15

Answer15

Part (b) · 2 marks

Expand and simplify the product (x + 5)(x − 4).

  1. 1(x + 5)(x − 4) = x² − 4x + 5x − 20
  2. 2= x² + x − 20

Answerx² + x − 20

Part (c) · 2 marks

Factorise the expression 21r³ − 7r.

  1. 1Common factor of 21r³ and 7r is 7r
  2. 221r³ − 7r = 7r(3r² − 1)

Answer7r(3r² − 1)

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Also searched as: 0580/13/O/N/25 · 0580_w25_qp_13 · 0580 w25 13 · question 17.
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