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

Last Updated: 02.07.2025 21:30

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

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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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Do people of NYC drive around Central Park all the time? Is there any subway tunnel to cross the park quickly? Is it annoying for people and does it cause traffic?

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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Move the nub up to the top:

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

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n^2 - 1

(n - 1)(n + 1)

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What are the potential economic consequences of the U.S. following Europe's lead on climate policies, as discussed in the article?

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

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

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