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

08.06.2025 01:28

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.

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

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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

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?

n^2 - n + n - 1

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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^2 - 1

What are some sad truths about life?

(n - 1)(n + 1)

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

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Move the nub up to the top: