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

15.06.2025 02:52

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

n^2 - n + n - 1

(n - 1)(n + 1)

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What can you do if you are a full-grown adult, but never experienced being a child?

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

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n^2 - 1

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

At what stage in your life did you realize, "No, I can't do this any more" and walk out? Why?

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

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What would happen if the Soviet Union had simply annexed Manchuria after World War 2 or kept it independent as a puppet state allied them and separate from China as China was too weak too oppose it anyway?

Move the nub up to the top:

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

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