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

16.06.2025 09:36

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

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

n^2 - 1

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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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(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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Move the nub up to the top:

Why can't NASA just bite the bullet and launch a plainly simple mission, audited by flat earther peers start to finish that definitively proves to even the smallest minds that the earth is an oblong spheroid, and not flat?

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

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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

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