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

13.06.2025 10:31

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

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:

(n - 1)(n + 1)

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

n^2 - 1

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

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

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n^2 - n + n - 1

Why do people keep saying they have evidence and have presented it that proves you're wrong even though they have none and haven't presented anything? Furthermore, what do they think you're wrong about?

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