Why is (n-1)(n+1)=n^2-1?
10.06.2025 17:10

xxxx
xxx x
n^2 - n + n - 1
Mega-Tsunamis That Shook the World for 9 Days Revealed in New Satellite Images - Gizmodo
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
Move the nub up to the top:
We Bought a ‘Peeing’ Robot Attack Dog From Temu. It Was Even Weirder Than Expected - WIRED
(n - 1)(n + 1)
n^2 - 1
And you are left with almost a square. One less than the square of side n.
Paris Erupts in Celebrations, Riots After PSG Wins Champions League - WSJ
xxxx
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
So, that’s a rectangle with sides 2 and 4.
The basic answer is that you cross-multiply the values in each factor:
xxx
xxx x
More Americans applied for jobless benefits last week, rising to highest level in eight months - PBS
xxx