Why is (n-1)(n+1)=n^2-1?

10.06.2025 05:40

Why is (n-1)(n+1)=n^2-1?

Move the nub up to the top:

n^2 - n + n - 1

n^2 - 1

Why do many people think that Japan is not a gay-friendly country whereas 72% Japanese support same-sex marriage (the same number as in the US)?

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The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2

Why is it after eating almonds when I’m occupied, I don’t feel mild itch, but as soon as I have nothing to do, I feel mildly itchy?

If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2

And you are left with almost a square. One less than the square of side n.

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(n - 1)(n + 1)

The basic answer is that you cross-multiply the values in each factor:

Why aren't U.S. prisons more like Marine Corps boot camp, were every second of the day there are mandatory activities so that at night everyone is so tired they go to sleep until wakeup at 5:30 am? Would this make prisons safer for all?

So, that’s a rectangle with sides 2 and 4.