Why is (n-1)(n+1)=n^2-1?
15.06.2025 05:12
The basic answer is that you cross-multiply the values in each factor:
xxx
Move the nub up to the top:
What is the worst name in Tolkien’s legendarium (meaning and look)?
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
xxx
n^2 - n + n - 1
Have you ever heard of the god Priapus being the same as the god Phosphorus?
So, that’s a rectangle with sides 2 and 4.
xxx x
(n - 1)(n + 1)
n^2 - 1
xxx x
xxxx
These glowing axolotls may hold the secret to human limb regeneration - The Washington Post
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
xx
And you are left with almost a square. One less than the square of side n.
xxxx