Prove that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.

A problem of this nature seems complex at first until you break it down and see what it is really asking you to find. We can represent two consecutive integers as x and x + 1. The problem asks us to prove something. It asks us to show that (x+1)2 - x2 is equal to the sum of x + (x+1) = 2x + 1.
Thanks to our notation, the answer falls into place quite easily. Expanding (x+1)2, as it is an algebraic identity, and solving for the difference between the two squares gives us the desired result.

Answered by Maths tutor

12204 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The equation of Line 1 is y=2x-2 and the equation of Line 2 is 2y-4x+5=0. Prove that these 2 lines are parallel to each other.


1/4 of a number is 20. What is 5 times the number?


A is the point (2,-5), B is the point (-1,4). (a) What is the gradient of the line passing through points A and B? (b) Does the point (-100,301) lie on the line passing through points A and B?


What is 3.25 plus 3 and 3/4?


We're here to help

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