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

10.06.2025 00:23

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

(n - 1)(n + 1)

Move the nub up to the top:

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

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Ok, so this is a question seeking an answer to clear up whatever gymnastics are in my head. I'm a moderately attractive guy, sincere heart, genuinely looking to love another, established. Why don't women that I'm attracted to, want me back?

n^2 - 1

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Why do we still feel attached or jealous when a covert narcissist moves on, even after realizing their toxicity and the suffering they caused?

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Are there many people here who suffer from schizophrenia?

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

n^2 - n + n - 1

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

Have you ever had a scary dream about a loved one or friend soon after their death?

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