Why is (n-1)(n+1)=n^2-1?

Last Updated: 02.07.2025 00:34

Why is (n-1)(n+1)=n^2-1?

If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2

xxxx

xxx x

Do marathon racing shoes like Nike Vaporfly and Alphafly provide an unfair advantage to runners over competitors who do not wear them?

So, that’s a rectangle with sides 2 and 4.

(n - 1)(n + 1)

xxx

Sharks Follow This Universal Math Rule, Confirming a Century-Old Law of Biology - SciTechDaily

The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2

The basic answer is that you cross-multiply the values in each factor:

Move the nub up to the top:

John Isner now ranks where Carlos Alcaraz's win over Jannik Sinner sits in the best matches ever, 'I'm changing my tune' - The Tennis Gazette

n^2 - n + n - 1

xxxx

xxx

Former MLB Star Suffers Serious Injury in Savannah Bananas Game - Sports Illustrated

xxx x

And you are left with almost a square. One less than the square of side n.

xx

Elon Musk posts throwback to SpaceX’s garage days after the 500th Falcon rocket launch; his caption reads - Times of India

n^2 - 1