Why is (n-1)(n+1)=n^2-1?
16.06.2025 00:32

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n^2 - 1
The basic answer is that you cross-multiply the values in each factor:
xx
xxx x
xxx
Is it possible to become homeless after being released from jail or prison in the United States?
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
xxx x
(n - 1)(n + 1)
Why is the government destroying the homeless instead of helping them?
n^2 - n + n - 1
So, that’s a rectangle with sides 2 and 4.
Move the nub up to the top:
Why don't some people like the 10 Commandments?
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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Why is the US going after Canada after all? What is the reason for all this hostility?
And you are left with almost a square. One less than the square of side n.