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

09.06.2025 00:02

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

xxxx

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

xx

Apple iPhone 17 Pro Max: The Best View Yet Of New Design Just Leaked - Forbes

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

(n - 1)(n + 1)

Grieving Woman Gets A Sign When Someone With Familiar 'Eyebrows' Pays A Visit - The Dodo - For Animal People

xxxx

Move the nub up to the top:

xxx x

Why are Republicans so brainwashed and oblivious to the fact that a lot of the price increases going on right now is due to corporate greed, not inflation?

n^2 - n + n - 1

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

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

Samsung is giving these Galaxy phones a big One UI upgrade - here's which models qualify - ZDNET

xxx

xxx x

n^2 - 1

‘Lilo & Stitch’ to Battle ‘Ballerina’ for Box Office Crown as ‘John Wick’ Spinoff Targets $30 Million Opening Weekend - Variety

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