Why is (n-1)(n+1)=n^2-1?
12.06.2025 00:53

xxxx
(n - 1)(n + 1)
n^2 - n + n - 1
The basic answer is that you cross-multiply the values in each factor:
xxx x
xx
Can you share a picture of your favorite outfit and explain why you love it?
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
xxx
Texas woman dies from brain-eating amoeba after cleaning sinuses with tap water - NBC News
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
xxx
xxxx
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.
Attenborough's Ocean a Brutal, Beautiful Wake-up Call - Newser
Move the nub up to the top: