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

13.06.2025 00:39

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

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n^2 - n + n - 1

How did your marriage end?

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(n - 1)(n + 1)

Is Matt Gaetz qualified to be Attorney General of the United States?

Move the nub up to the top:

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

n^2 - 1

My religion teacher said that there are no atheists because in order to reject God, you must first have a concept of God, and if you have a concept of God, you are not an atheist. In what way is this true, if at all? Why?

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

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Who is the greatest light welterweight boxer of all time?

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

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Do you enjoy cheating on your spouse? If so, why?

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