4MA1/2HR Jan 2020, Question 25: 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
Given N is a multiple of 5, with A = N + 1 and B = N − 1, use algebra to show A² − B² is always divisible by 20.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1A² = (N + 1)² = N² + 2N + 1 and B² = N² − 2N + 1
- 2A² − B² = 4N
- 3N is a multiple of 5, so N = 5k and 4N = 20k
- 4So A² − B² is always a multiple of 20
AnswerA² − B² is always a multiple of 20
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 2020 · 4MA1/2HR · 4ma1 jan20 2hr · question 25.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.