4MA1/2HR Jan 2021, Question 15: Expand and Simplify
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Prove algebraically that multiplying any two odd numbers always gives an odd number.
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Solution · 4 marks
- 1Any two odd numbers can be written 2m + 1 and 2n + 1, for integers m and n
- 2(2m + 1)(2n + 1) = 4mn + 2m + 2n + 1
- 3= 2(2mn + m + n) + 1, which is 2 × integer + 1
- 4So (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1, which is odd
Answer(2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1, which is odd
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