Why is (n-1)(n+1)=n^2-1?
Last Updated: 18.06.2025 02:22

The basic answer is that you cross-multiply the values in each factor:
n^2 - n + n - 1
xxxx
What have I done wrong? How can I start over?
And you are left with almost a square. One less than the square of side n.
xxxx
xx
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
So, that’s a rectangle with sides 2 and 4.
xxx x
Move the nub up to the top:
n^2 - 1
xxx
Do you think Japan will have same-sex marriage by 2030?
xxx x
(n - 1)(n + 1)
xxx
How did the Nazis figure out whether a person or community is 'Aryan' or not?
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2