Why is (n-1)(n+1)=n^2-1?
11.06.2025 00:06

Move the nub up to the top:
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
xxxx
Why does a narcissist act like it's nothing when they hurt you?
xxx x
n^2 - n + n - 1
The basic answer is that you cross-multiply the values in each factor:
xxx x
xxxx
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
Feds poised to approve SpaceX’s takeover of another military launch pad - Ars Technica
xxx
(n - 1)(n + 1)
xxx
xx
And you are left with almost a square. One less than the square of side n.
n^2 - 1
Popular sugar substitute erythritol may impair brain blood vessel health, study finds - PsyPost
So, that’s a rectangle with sides 2 and 4.