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

10.06.2025 15:50

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

n^2 - n + n - 1

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

Move the nub up to the top:

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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 - 1

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

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

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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Why do people who aren't trans feel the need to put pronouns next to their name or picture? It seems so cringeworthy to me, to participate in that SJW paradigm of thought, like they are a spineless person who just goes along with the trends.

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Has Messi scored against the Buffon?

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