4MA1/1H Jun 2021, Question 17: Expand and Simplify
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks
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The question, in short
Using algebra, prove that for any 3 consecutive even numbers, the largest squared minus the smallest squared equals 8 times the middle number.
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Solution · 3 marks
- 1Let the three consecutive even numbers be 2n, 2n + 2, 2n + 4
- 2(2n + 4)² − (2n)² = (4n² + 16n + 16) − 4n² = 16n + 16
- 38 times the middle number = 8(2n + 2) = 16n + 16
- 4Since both expressions are equal, the statement is proven
AnswerCorrectly shown
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