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

Last Updated: 03.07.2025 02:07

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

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

Move the nub up to the top:

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

n^2 - 1

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

If the United States leaves the EU to fend for themselves in the economy and NATO, could Europe become irrelevant in the global economy compare to China and America dominance in the world stage in AI and semiconductors? Will Europe become cash poor?

n^2 - n + n - 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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(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

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