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

12.06.2025 13:09

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

(n - 1)(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

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

Why am I always so tired, no matter how much I sleep?

Move the nub up to the top:

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Why cant I feel anything in my sleep? I cannot even feel myself moving, breathing, and swallowing saliva! I cannot even hear anything, not even my alarm! Some people that I've been with says that I'm moving a lot in my sleep, how can I stop it?

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

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n^2 - n + n - 1

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n^2 - 1