Why is (n-1)(n+1)=n^2-1?
Last Updated: 22.06.2025 06:35
The basic answer is that you cross-multiply the values in each factor:
xx
xxxx
Dozens of Hooters locations abruptly closed: List of latest closures - 9News
n^2 - 1
Move the nub up to the top:
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
Manny Machado, pitching power Padres to series win over Brewers - San Diego Union-Tribune
xxx
xxx x
n^2 - n + n - 1
Weber, Morgan health officials warn residents after bat tests positive for rabies - KSL.com
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
(n - 1)(n + 1)
xxx
So, that’s a rectangle with sides 2 and 4.
xxx x
And you are left with almost a square. One less than the square of side n.
xxxx