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

Last Updated: 02.07.2025 03:42

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

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

xx

xxxx

Steelers players defend attending Trump rally at U.S. Steel plant: 'I'm not apologetic about that' - Pittsburgh Post-Gazette

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

xxx

xxx

If Russia needs the resources to fund the war in Ukraine, why doesn’t it throw open its doors to visa free western tourism? Enough people would be interested, & it would start to get some hard currency as €, CHF, £, SEK, $, JPY in the tills at shops.

xxx x

n^2 - n + n - 1

xxxx

Titan's Atmosphere 'Wobbles Like a Gyroscope' – And No One Knows Why - ScienceAlert

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

(n - 1)(n + 1)

xxx x

Antarctic detector picks up signals that defy all known laws of particle physics - Interesting Engineering

Move the nub up to the top:

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:

NASA’s Chandra Sees Surprisingly Strong Black Hole Jet at Cosmic “Noon” - NASA (.gov)

n^2 - 1