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

10.06.2025 10:48

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

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Billionaire BlackRock CEO Larry Fink Warns $36,000,000,000,000 Debt Will ‘Overwhelm’ America Unless Stellar Economic Growth Achieved - The Daily Hodl

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

n^2 - 1

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‘King of the Hill’ creators slammed for ‘pathetic’ Jonathan Joss tribute after his murder - New York Post

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

n^2 - n + n - 1

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Move the nub up to the top:

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(n - 1)(n + 1)

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