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

14.06.2025 05:39

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

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 - 1

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(n - 1)(n + 1)

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

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

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

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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 - n + n - 1

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Relocating to Sweden to save money. I got a job offer of 47000SEK before tax, visas sponsored for my wife & my mother (with a laryngectomy). My wife, a general medicine graduate, wants to specialize in Sweden. Can we live well and save 4000€ monthly?

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