Why is (n-1)(n+1)=n^2-1?
12.06.2025 01:05

The basic answer is that you cross-multiply the values in each factor:
(n - 1)(n + 1)
n^2 - 1
What’s something you did a lot as a kid that you don’t miss now that you’re an adult?
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.
xxx
Graphene Is Stretchable? Physicists Make “Miracle Material” Bend Like Never Before - SciTechDaily
xxx x
Move the nub up to the top:
xx
And you are left with almost a square. One less than the square of side n.
n^2 - n + n - 1
xxxx
AI Links Early Life Risks to Behavioral Challenges at Age Five - Neuroscience News
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
xxx
xxx x