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

13.06.2025 12:25

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

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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

What does it mean when a British person says "I can't be asked"?

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

(n - 1)(n + 1)

You found a love potion, and your friend tried to use it on an attractive popular girl, but he accidentally dropped it on the neighbors dog. Now the dog won't stop following him. How would you help him?

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n^2 - 1

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Joe Biden is not the best president we had. That would be John F. Kennedy. How is voting for Donald Trump any worse than voting for Joe Biden?

Move the nub up to the top:

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

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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

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