Why is (n-1)(n+1)=n^2-1?
13.06.2025 19:07

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n^2 - 1
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(n - 1)(n + 1)
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What do you think is the most powerful line in the song "Non, Je Ne Regrette Rien" by Édith Piaf?
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
The basic answer is that you cross-multiply the values in each factor:
n^2 - n + n - 1
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And you are left with almost a square. One less than the square of side n.
So, that’s a rectangle with sides 2 and 4.
Move the nub up to the top:
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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