4024/12 Oct/Nov 2025, Question 16: Expanding Two Brackets
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Expand and simplify a product of two surd brackets, then rationalise a fraction with a surd denominator.
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Part (a) · 2 marks
Expand and simplify (3 + √2)(1 + 4√2).
- 1(3 + √2)(1 + 4√2) = 3 + 12√2 + √2 + 4 × 2
- 2= 3 + 13√2 + 8
- 3= 11 + 13√2
Answer11 + 13√2
Part (b) · 2 marks
Rationalise the denominator of 1/(1 + √7).
- 1Multiply top and bottom by (√7 − 1)
- 21/(1 + √7) × (√7 − 1)/(√7 − 1) = (√7 − 1)/(7 − 1)
- 3= (−1 + √7)/6
Answer(−1 + √7)/6
Stuck on a step? Read the free lesson: Expanding Two Brackets
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Also searched as: 4024/12/O/N/25 · 4024_w25_qp_12 · 4024 w25 12 · question 16.
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