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

11.06.2025 08:34

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

n^2 - n + n - 1

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Do people really never face any hidden costs or surprises with surgeries in countries with single-payer healthcare like the NHS?

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n^2 - 1

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

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I’ve often wondered why fans aren’t deployed on GBBO during warm weather? I’ve seen too many desserts melt (and bakers too…). (I live in Pompano Beach and we try to use fans in lieu of AC as much as possible).

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(n - 1)(n + 1)

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

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