Why is (n-1)(n+1)=n^2-1?
10.06.2025 04:29

xxx
(n - 1)(n + 1)
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
Precision Spectroscopy Reaffirms Gap Between Theory and Experiment - American Physical Society
n^2 - 1
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:
Super Again: UNC Storms Past Oklahoma in NCAA Regional Finale - 247Sports
The basic answer is that you cross-multiply the values in each factor:
xxx x
xxx x
xxxx
xxx
xxxx
How do empaths destroy narcissists?
xx
So, that’s a rectangle with sides 2 and 4.
n^2 - n + n - 1
And you are left with almost a square. One less than the square of side n.