Why is (n-1)(n+1)=n^2-1?
Last Updated: 02.07.2025 05:50
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:
xxx x
The basic answer is that you cross-multiply the values in each factor:
n^2 - 1
xxxx
xxxx
xx
xxx
And you are left with almost a square. One less than the square of side n.
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
'Call of Duty: Black Ops 7' to Star Milo Ventimiglia, Kiernan Shipka - Variety
So, that’s a rectangle with sides 2 and 4.
n^2 - n + n - 1
xxx
(n - 1)(n + 1)