prove that any odd number squared is one more than a multiple of four.

any odd number can be written as (2n+1), where n is any integer (whole number). Squaring any odd number is therefore= (2n+1)2 . expanding the brackets gives =4n2+2n+2n+12 = 4n2+4n+1. factorising the 4 out of the first two terms gives =4(n2+n)+1. 4(n2+n) is a multiple of 4 due to the factored out 4, and the +1 after means that any odd number squared is one more than a multiple of 4.

HJ
Answered by Harry J. Maths tutor

2627 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

There are 10 boys and 20 girls in a class. The mean mark for the class is 60, the mean mark for the girls is 54. Work out the mean mark for the boys.


Clare buys some shares for $50x. Later, she sells the shares for $(600 + 5x). She makes a profit of x% (a) Show that x^2 + 90x − 1200 = 0


A person leaves their flat at 8:00am and travels to work at an average speed of 32 mph. They arrive at work at 9:15am. Calculate the distance they travel to work.


Solve: (6x + 4)/(2x - 2) + 6 = 8


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