Why is (n-1)(n+1)=n^2-1?
Last Updated: 02.07.2025 10:12
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
xxx x
n^2 - n + n - 1
What do you think of Sony's generative AI rendering Aloy in a Horizon: Forbidden West demo?
xxx
xxx
n^2 - 1
(n - 1)(n + 1)
And you are left with almost a square. One less than the square of side n.
Move the nub up to the top:
What are the ways in which the human body adapts to different climates and heat?
The basic answer is that you cross-multiply the values in each factor:
So, that’s a rectangle with sides 2 and 4.
xxx x
xxxx
xxxx
xx
Your Brain Has a Hidden Rhythm, And It May Reveal How Smart You Are - ScienceAlert
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2