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

10.06.2025 01:14

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

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

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

Move the nub up to the top:

The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2

Why is it that when the Democrats absolutely love everyone to be LGBTP, they don't even acknowledge that Barack Obama and his husband Big Mike are homosexual, and he is the first homosexual president of the USA?

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

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n^2 - n + n - 1