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

Last Updated: 26.06.2025 09:50

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

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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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?

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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Who is your favorite young adult author and what is your favorite book by them? What makes it stand out from their other works?

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n^2 - 1

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

n^2 - n + n - 1

Move the nub up to the top:

What happens when you need emergency surgery in countries with universal healthcare vs the US?

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(n - 1)(n + 1)

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