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

Last Updated: 19.06.2025 12:25

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

Move the nub up to the top:

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

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

Which current F1 drivers should switch teams based on historical patterns?

n^2 - 1

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Why do entitled people demand that I pick up after my doggo when he goes to the bathroom? Do they not know that doggy doo decomposes & feeds the plants?

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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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n^2 - n + n - 1

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(n - 1)(n + 1)

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

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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