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

Last Updated: 19.06.2025 11:28

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

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

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n^2 - 1

Move the nub up to the top:

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

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(n - 1)(n + 1)

n^2 - n + n - 1

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I committed the unpardonable sin. God immediately punished me so that I can no longer think like before and my brain is as if paralyzed and does not work. I've tried everything (confession, repentance, etc.) nothing helps. Any advice?

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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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.

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