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

Last Updated: 26.06.2025 00:49

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

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

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

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n^2 - 1

(n - 1)(n + 1)

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n^2 - n + n - 1

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Move the nub up to the top:

The Roman Empire at the time of Christ kept meticulous records. Why then, is there no record of the trial of Jesus?

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