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

12.06.2025 04:07

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

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

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

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n^2 - 1

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(n - 1)(n + 1)

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Move the nub up to the top:

Why do some people feel down in summer, specifically in July and August? What could be the reasons behind this feeling of sadness during those months only?

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

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