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

11.06.2025 09:33

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

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

(n - 1)(n + 1)

Move the nub up to the top:

How do you emotionally react to when others seem to feel sorry for you?

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 - 1

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What is the cost of implementing synchronized traffic lights in a mid-sized city?

n^2 - n + n - 1

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Elon Musk threatened to decommission Dragon spacecraft. Here's what that would mean for NASA - ABC News

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

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Why do people procrastinate and how can they stop?

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

What should I expect after a BBL surgery?

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