Why is (n-1)(n+1)=n^2-1?
12.06.2025 00:03

xxxx
xxx x
xxx
Robotic table tennis system predicts ball trajectory and adapts swing in real time - Tech Xplore
(n - 1)(n + 1)
The basic answer is that you cross-multiply the values in each factor:
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
n^2 - 1
Why are the democrats keep insisting that there are more than two genders?
xxx
xxx x
Move the nub up to the top:
What transforms the philosophical intellect?
And you are left with almost a square. One less than the square of side n.
So, that’s a rectangle with sides 2 and 4.
xx
n^2 - n + n - 1