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

12.06.2025 09:16

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

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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What is price of the "liberal celebrities" e.g. Bill Maher, Seth Meyers, Jon Stewart, Trevor Noah, Jimmy Kimmel, Desi Lydic etc. to join the great MAGA movement like Stephen Colbert who wanted to European ambassadorship to turn back on "the Left"?

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

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

n^2 - 1

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Move the nub up to the top:

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

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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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n^2 - n + n - 1

(n - 1)(n + 1)

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