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

09.06.2025 01:40

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

(n - 1)(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^2 - n + n - 1

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Move the nub up to the top:

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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

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

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When a dog smells another dog’s poo or wee, do they then remember that scent for when they smell it again, or even further know which dog they are smelling if they know the dog?

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