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

15.06.2025 11:51

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

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

Move the nub up to the top:

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n^2 - n + n - 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

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I’m a 25 year old teacher teaching at boys school & I have colleagues younger than me. I caught one of my students telling her he wanted her as his teacher instead & it hurt my feelings. They compliment her a lot. It makes me jealous. What do I do?

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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

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

n^2 - 1

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

(n - 1)(n + 1)

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Why am I so triggered and depressed over a minor thing?

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