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

12.06.2025 05:25

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

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

n^2 - 1

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n^2 - n + n - 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

Why can't the ISS take a picture of Earth and prove to the Flat Earth Society that Earth is not really flat?

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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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Why do people hate Nickelback so much? What makes them different from other popular bands like Linkin Park, Green Day, etc.? Is it just because they're Canadian or what?

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

(n - 1)(n + 1)

Why do I randomly start sweating a lot in public (while waiting in line, in a new class, etc.) then start sweating more because I’m embarrassed that I’m sweating so much? Is this social anxiety?

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

Move the nub up to the top:

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