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

Last Updated: 19.06.2025 04:46

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

Move the nub up to the top:

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

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

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Why do trans people get so deeply offended when a stranger misgenders them, especially when it's a first encounter? I've been socially transitioned for 4 years and it just feels like a waste of energy to be so hurt by it.

(n - 1)(n + 1)

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

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n^2 - 1

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Why are details for questions here on Quora so limited? I have an account here on Quora and Yahoo Answers. I like discussing different subjects.

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