Why is (n-1)(n+1)=n^2-1?
10.06.2025 00:48

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
xxx
Does being poor build better character than being born rich?
xx
xxx x
(n - 1)(n + 1)
Mario Kart World: All Costume Unlocks & Complete Outfit List - Nintendo Life
n^2 - 1
And you are left with almost a square. One less than the square of side n.
xxxx
So, that’s a rectangle with sides 2 and 4.
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
xxx x
What's it like to have an IQ of 140 to 170? Do people notice you're different?
Move the nub up to the top:
xxx
The basic answer is that you cross-multiply the values in each factor:
n^2 - n + n - 1