Why is (n-1)(n+1)=n^2-1?
Last Updated: 30.06.2025 03:48

n^2 - n + n - 1
xxxx
Move the nub up to the top:
FDA Gives Tomato Recall Over Salmonella Highest Risk Warning - TODAY.com
xxx x
So, that’s a rectangle with sides 2 and 4.
xxx
(n - 1)(n + 1)
xx
And you are left with almost a square. One less than the square of side n.
Stock futures fall as investors eye Israel-Iran conflict: Live updates - CNBC
xxxx
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
xxx x
n^2 - 1
xxx
Are British people in awe when someone from the United States visits their country?
The basic answer is that you cross-multiply the values in each factor: