Prove that the square of an odd number is always 1 more than a multiple of 4. [Edexcel Higher Tier 2018, Paper 1: Question 12]

We want to start with “the square of an odd number” and show something. Remember that any odd number can be expressed as 2n+1 (an even number is 2n, and any odd number is 1 larger than an even). So squaring an odd number gives us (2n+1)2.Let’s see if we can evaluate this algebraically to get what the question asks for. Firstly we need to expand the brackets:(2n+1)2 = (2n)2 + 2(2n)(1) + 12            [by hairpin/FOIL method or the trick for squaring brackets] = 4n2 + 4n + 1Now notice the factor of 4 in two of the terms; we can factorise! = 4(n2+n) + 1which is something times 4, plus 1; i.e. “1 more than a multiple of 4”. This is the proof the question required, and is general for any odd number 2n+1.

Answered by Robert H. Maths tutor

2295 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Simplify the expression: (x^2 + x - 6)/(3x^2 + 9x)


What is the cosine rule?


Prove that the square of an odd number is always one more than a multiple of 4


A is the point with coordinates (5, 9) B is the point with coordinates (d, 15) The gradient of the line AB is 3 Work out the value of d.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences