4MA1/2HR Jan 2023, Question 19: Expand and Simplify
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Use algebra to show a relationship between the squares of the first and third of three consecutive even numbers and twice the square of the middle one.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Let the three consecutive even numbers be 2n, 2n + 2, 2n + 4
- 2(2n)² + (2n + 4)² = 4n² + (4n² + 16n + 16) = 8n² + 16n + 16
- 32 × (2n + 2)² = 2 × (4n² + 8n + 4) = 8n² + 16n + 8
- 4(8n² + 16n + 16) − (8n² + 16n + 8) = 8
- 5So the sum of the squares of the smallest and largest is 8 more than twice the square of the middle
AnswerCorrectly shown
Stuck on a step? Read the free lesson: Expand and Simplify
Practise more expand and simplify questions
Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on expand and simplify
Also searched as: 4MA1 2HR January 2023 · 4MA1/2HR · 4ma1 jan23 2hr · question 19.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.