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

Last Updated: 18.06.2025 04:30

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 - 1)(n + 1)

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

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.

Why are people so rude to debt collector’s? I am one and I am so tired of being mistreated. We are under paid and then have to deal with the most ungrateful, and disrespectful people. We aren’t customer service. Don’t get mad at us because YOU owe.

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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Move the nub up to the top:

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n^2 - 1

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n^2 - n + n - 1