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

08.06.2025 00:51

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

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

n^2 - n + n - 1

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(n - 1)(n + 1)

One day, I happened to walk past where my crush was with friends. Then all of a sudden they start laughing, and someone maybe him, goes "freaking (my name) with her freaking hair!" Can anyone offer insights into this? We're in middle school.

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

California schools are very liberal. Do you think California schools are teaching students to hate Republican views (views on: God, guns, prayer, secure borders, etc.)?

Move the nub up to the top:

n^2 - 1

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