Why is (n-1)(n+1)=n^2-1?
13.06.2025 02:07

(n - 1)(n + 1)
xxx
Move the nub up to the top:
n^2 - 1
xxx x
So, that’s a rectangle with sides 2 and 4.
What baseball stories from the early days of the sport seem too bizarre to be true?
And you are left with almost a square. One less than the square of side n.
The basic answer is that you cross-multiply the values in each factor:
xxx x
Why am I so tired of seeing homeless people all over the place?
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
xx
xxx
How often do prisoners try to escape from jail/prison, and how many of them succeed?
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
xxxx
xxxx
n^2 - n + n - 1