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

11.06.2025 02:54

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

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

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n^2 - 1

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

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)

Why does my crush make me jealous about having a girlfriend?

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Move the nub up to the top:

How do I stop having work crushes because I only keep getting disappointed almost every day as I keep seeing they don’t like me back and won’t ever ask me out?

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n^2 - n + n - 1

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

How will Israelis respond to someone claiming that anti-Zionism is not anti-Semitism, in the same way as anti-feminism not being misogyny and opposing same-sex marriage not being homophobia?

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