Prove that the square of an odd number is always 1 more than a multiple of 4

In order to prove this we can write a general expression of an odd number in terms of n, e.g - 2n+1Square this 'odd number': (2n+1)^2, therefore you can write it as (2n+1)(2n+1), then expand (multiply out) the brackets to get: 4n^2 + 4n + 1We can then factorise this to get: 4(n^2 + 1) + 1 which is 'one more than a multiple of 4' as 4(n^2 + 1) will always be a multiple of 4 regardless of what n is.

BH
Answered by Ben H. Maths tutor

2743 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the two simultaneous equations. 1. x^2 + y^2 = 25, 2. y - 3x = 13


Ayo is 7 years older than Hugo. Mel is twice as old as Ayo. The sum of their three ages is 77 Find the ratio of Hugo's age to Ayo's age to Mel's age.


Solve 8x + 9y = 3 and x + y = 0.


How to solve a quadratic equation.


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 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences