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

Last Updated: 22.06.2025 00:08

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

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Why do many Hong Kong Chinese look different from the Han Chinese in mainland China?

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

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Why do I feel worthless most of the time?

Move the nub up to the top:

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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

What’s the craziest thing you’ve heard pretending to be asleep?

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

(n - 1)(n + 1)

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

Why do some people hesitate to say 'I love you' even after their partners have said it first? How can one interpret this behavior from their loved ones?

n^2 - n + n - 1

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

n^2 - 1

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