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

10.06.2025 12:17

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

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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

Move the nub up to the top:

My marriage is fixed. My future husband repeatedly calls me to meet me in private and pressure me to have a relationship. What should I do?

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n^2 - 1

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

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

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(n - 1)(n + 1)

Why, after a divorce, would one still want to ruin the other one’s life?

n^2 - n + n - 1

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

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What were the career paths of each member of "The Monkees" after the band disbanded? Did any of them have successful music careers?

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