4MA1/1HR Jun 2025, Question 17: Expand and Simplify
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks
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The question, in short
Using algebra, prove that squaring the largest and smallest of any three consecutive multiples of 4 gives a difference that is always a multiple of 64.
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Solution · 3 marks
- 1Let the numbers be 4n, 4n + 4, 4n + 8
- 2(4n + 8)² − (4n)²
- 3= 16n² + 64n + 64 − 16n²
- 4= 64n + 64
- 5= 64(n + 1), which is a multiple of 64
Answer(4n + 8)² − (4n)² = 64n + 64 = 64(n + 1), a multiple of 64
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