Why is (n-1)(n+1)=n^2-1?
Last Updated: 02.07.2025 00:18

xx
n^2 - n + n - 1
(n - 1)(n + 1)
Star Trek: Strange New Worlds is getting a fifth and final season - The Verge
So, that’s a rectangle with sides 2 and 4.
The basic answer is that you cross-multiply the values in each factor:
xxx
Hundreds of families displaced by Israeli air strikes on Gaza, witnesses say - BBC
xxx
And you are left with almost a square. One less than the square of side n.
xxxx
World fertility rates in 'unprecedented decline' - UN - BBC
Move the nub up to the top:
xxx x
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
Trump insults Powell again as another top Fed official joins the call to lower interest rates - CNN
xxxx
xxx x
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
n^2 - 1