Why is (n-1)(n+1)=n^2-1?
Last Updated: 03.07.2025 00:31
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
So, that’s a rectangle with sides 2 and 4.
xxxx
And you are left with almost a square. One less than the square of side n.
(n - 1)(n + 1)
‘Stranger Things’ Season 5 Gets Three-Part Release, Series Finale Set for New Year’s Eve - Variety
xxx x
The basic answer is that you cross-multiply the values in each factor:
xxxx
Move the nub up to the top:
xxx x
n^2 - 1
Fast Radio Bursts Reveal Where The Universe's Missing Matter Is Hiding - ScienceAlert
xx
xxx
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
After 70 years of the crappiest computers ever made, why does IBM exist?
n^2 - n + n - 1