Logo

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

12.06.2025 07:32

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

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

xxx

xxx

‘King of the Hill’ creators slammed for ‘pathetic’ Jonathan Joss tribute after his murder - New York Post

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

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

xxxx

Scientists Uncover a Lost World Hidden Beneath Antarctica’s Frozen Tapestry for Millions of Years - Indian Defence Review

(n - 1)(n + 1)

Move the nub up to the top:

xx

Internal document shows how UnitedHealth executives prepared to tamp down investor unrest - statnews.com

xxx x

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

n^2 - 1

The Best Of Roots Picnic Made Up For The Absolute Worst - HuffPost

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

xxxx

xxx x

Why do people turn a blind eye to bad behaviour if someone is very good looking? Whereas if someone is ugly, they get harshly judged for everything?

n^2 - n + n - 1