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

10.06.2025 08:16

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

(n - 1)(n + 1)

n^2 - 1

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Trump administration prepares to ease big bank rules - Politico

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

If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2

"People don't even like him": Musk becomes GOP pariah after "ridiculous" Trump attacks - Axios

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

n^2 - n + n - 1

Billy Joel cracking jokes about ‘getting old,’ ‘cremated’ after brain disorder diagnosis, Tribeca doc director shares - New York Post

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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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Wall Street sets Palantir stock price for next 12 months - Finbold

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Move the nub up to the top:

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