Why is (n-1)(n+1)=n^2-1?
13.06.2025 02:40

If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
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:
Thousands of Netflix fans gather for Tudum - TechCrunch
(n - 1)(n + 1)
xxx x
xxxx
xxx
So, that’s a rectangle with sides 2 and 4.
n^2 - 1
‘Smash’ abruptly announces final show after Tony Awards drama in Broadway shocker - New York Post
xxx
Move the nub up to the top:
xxxx
Do women like watching men sucking men?
xxx x
And you are left with almost a square. One less than the square of side n.
xx
Aston Martin reveals track-day version of Valkyrie Le Mans Hypercar - Motorsport.com
n^2 - n + n - 1