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

Last Updated: 29.06.2025 01:54

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

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(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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Who are the main characters of Family Guy, American Dad, and King of the Hill? Who are the recurring characters of family guy, American dad, and king of the hill? What changes will be made in all 3 shows?

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Move the nub up to the top:

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

n^2 - n + n - 1

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

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n^2 - 1

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