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

12.06.2025 00:56

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

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.

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n^2 - 1

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n^2 - n + n - 1

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I'm very sick. 72 years old. I thinking I'm losing my mind. My dead friend told me it's going to be okay. I could feel him. There is more…I don't know what but more.

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

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