Why is (n-1)(n+1)=n^2-1?
12.06.2025 03:54

The basic answer is that you cross-multiply the values in each factor:
xxxx
So, that’s a rectangle with sides 2 and 4.
AI could solve puzzles posed by twin stars in 'mere minutes or seconds on a single laptop' - Space
And you are left with almost a square. One less than the square of side n.
n^2 - n + n - 1
xx
Inside ‘Inside the NBA’ Transition to ESPN - Front Office Sports
xxx
n^2 - 1
xxx
Lions Make Surprise OL Signing to Replace Frank Ragnow - Detroit Jock City
xxx x
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 x
Move the nub up to the top:
xxxx
(n - 1)(n + 1)
Why do White people love dogs more than humans?
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2