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

Last Updated: 01.07.2025 15:14

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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How do you cope when your mother doesn't love you?

n^2 - n + n - 1

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How would you feel if your friend confided in you that she is cheating on her husband, knowing that he loves her deeply? What emotional and ethical considerations would you grapple with in response to her revelation?

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

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Move the nub up to the top:

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

n^2 - 1

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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

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

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Is Florida now unsurvivable because it's an oven due to climate change? It's 11:48 am on May 30th and the heat index in SoFla is 100. I can see it going up to over 130 by July.

(n - 1)(n + 1)