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

11.06.2025 11:13

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

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n^2 - 1

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

Would you date/marry a guy younger than you? If no, why not?

n^2 - n + n - 1

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

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A Biologist Spotlights The World’s Most Aggressive Bird. Hint: It’s Flightless, It’s Not The Ostrich, And It’s Been Known To Kill People - Forbes

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Move the nub up to the top:

The Trump admin ordered a coal power plant to stay on past retirement. Customers in 15 states will foot the bill - CNN

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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

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

Will you share your wife? Can she take both of us at the same time?

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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)

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