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

15.06.2025 05:34

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

Move the nub up to the top:

(n - 1)(n + 1)

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Are today’s baseball pitchers faster than a few years ago, or is it that radar guns have improved and get the pitch speed as it is released rather than as it reaches the plate?

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.

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

n^2 - 1

How do professional musicians handle their equipment during gigs? Do they bring their own or use the venue's sound system?

n^2 - n + n - 1

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

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