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

09.06.2025 04:39

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

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(n - 1)(n + 1)

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What story do you have involving a public restroom?

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

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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

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

n^2 - 1

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

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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

n^2 - n + n - 1

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