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

Last Updated: 17.06.2025 08:55

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

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

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 - 1)(n + 1)

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Did you know God exists? 900+ answers later and no atheist has yet to be successful. Day 8 of asking Atheists to provide a SINGLE argument that demonstrates a cause for the beginning of the universe while avoiding the problem of infinite regression.

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

n^2 - 1

n^2 - n + 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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Move the nub up to the top: