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

Last Updated: 29.06.2025 07:33

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

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Move the nub up to the top:

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n^2 - n + n - 1

n^2 - 1

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How did the pre US Civil War southern fire- eaters manage to so wildly miscalculate the consequences of secession?

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

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

(n - 1)(n + 1)

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

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

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?

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