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

11.06.2025 03:14

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

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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

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^2 - n + n - 1

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

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(n - 1)(n + 1)

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

Have you ever met someone and something seemed so unusual about them but you couldn't put your finger on what it was?

Move the nub up to the top:

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n^2 - 1

What were the first few days, weeks, months and then years like after finding out about your spouses infidelity? How did your feelings, and yours & their approach to the situation change in the immediate aftermath compared to later down the line?

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