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

14.06.2025 09:51

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

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

Move the nub up to the top:

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n^2 - 1

(n - 1)(n + 1)

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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.

If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2

If Donald Trump is so evil and Joe Biden is so good why is Trump the one selflessly providing Bibles for the needy while Biden doesn't? Why doesn't Biden care for America's spiritually needy people as much as Trump?

n^2 - n + n - 1

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

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