Why is (n-1)(n+1)=n^2-1?
10.06.2025 00:19

n^2 - n + n - 1
The basic answer is that you cross-multiply the values in each factor:
n^2 - 1
xxx
xxx x
xxxx
Does the West have a defense against China's PL17 air-air missile?
xx
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
Joni Ernst Issues Non-Apology for Joke About People Dying Due to GOP Medicaid Cuts - Rolling Stone
xxxx
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
And you are left with almost a square. One less than the square of side n.
xxx
(n - 1)(n + 1)
Move the nub up to the top:
Inside ‘Inside the NBA’ Transition to ESPN - Front Office Sports
So, that’s a rectangle with sides 2 and 4.