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

11.06.2025 05:15

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

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n^2 - 1

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Why do some people refuse to explain their actions or behavior when asked? Why do they claim to not know the reason instead of providing an explanation?

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

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

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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

n^2 - n + n - 1

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

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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

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(n - 1)(n + 1)

Move the nub up to the top:

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