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

12.06.2025 11:05

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

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.

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

n^2 - 1

Why did my ex of 2 years move on so fast after he left me? Why does he act so cold towards me, and as if I don't exist?

n^2 - n + n - 1

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Move the nub up to the top:

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(n - 1)(n + 1)

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

How was your JEE Mains 2024 April attempt?

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