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

13.06.2025 04:14

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

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n^2 - 1

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Why do I sweat so much? I’m 17 but I feel like I always need to re-apply deodorant and I am always self-conscious that I smell because I feel sweat under my arms.

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

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?

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

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(n - 1)(n + 1)

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

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n^2 - n + n - 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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Move the nub up to the top: