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

12.06.2025 01:14

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

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n^2 - n + n - 1

Do airline pilots try to avoid turbulence? How can you tell if your flight has been rerouted due to weather conditions or other factors?

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

Move the nub up to the top:

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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?

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

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

n^2 - 1

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(n - 1)(n + 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