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

Last Updated: 17.06.2025 11:47

Why is (n-1)(n+1)=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

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n^2 - 1

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

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

Move the nub up to the top:

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(n - 1)(n + 1)

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

n^2 - n + n - 1

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Why cant I breathe when I sleep on my back, I can breathe if im on my side or stomach but I feel uncomfortable since either my neck is twisted or my back is in pain, im physically healthy and my surroundings are clean so whats the problem?

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