Why is (n-1)(n+1)=n^2-1?
09.06.2025 12:03

xxx
xxx
(n - 1)(n + 1)
The #1 Anti-Inflammatory Diet Habit You Should Start, According to Dietitians - EatingWell
n^2 - n + n - 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
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
Becky Lynch wins the Intercontinental title at Money in the Bank - Cageside Seats
n^2 - 1
Move the nub up to the top:
xxxx
'Club World Ca$h Grab': Players don protest shirts at pregame - Sounder at Heart
xx
And you are left with almost a square. One less than the square of side n.
xxx x
No Social Security Payments for 12 Days: June 2025 Schedule Explained - Fingerlakes1.com
So, that’s a rectangle with sides 2 and 4.
xxxx
The basic answer is that you cross-multiply the values in each factor:
xxx x