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

12.06.2025 05:56

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

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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 - n + n - 1

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Who believes that Speaker Mike Johnson will certify ‘a free and fair and legal election'? Who believes that Speaker Mike Johnson will NOT certify ‘a free and fair and legal election'? Why?

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Move the nub up to the top:

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

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

n^2 - 1

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(n - 1)(n + 1)

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

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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