Why is (n-1)(n+1)=n^2-1?
09.06.2025 11:11

The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
Move the nub up to the top:
xxx
n^2 - 1
xxx x
(n - 1)(n + 1)
What is the best case of “You just picked a fight with the wrong person” that you've witnessed?
xx
xxx x
xxx
xxxx
xxxx
n^2 - n + n - 1
Are judges being lenient on hard criminals?
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:
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
So, that’s a rectangle with sides 2 and 4.