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

13.06.2025 04:50

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

The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2

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

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How did a computer scientist such as Geoffrey Hinton manage to win a Nobel Prize in physics when computer science already has its own Nobel Prize equivalent in the Turing Awards?

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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

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

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

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(n - 1)(n + 1)

Move the nub up to the top:

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Why do programmers choose to write their own code instead of using code that is already available online?

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n^2 - n + n - 1

n^2 - 1

From an axiology/value theory point of view, how can one say that a diverse society is better than a uniform one, especially given the negative effects of diversity (racism, sectarian conflict, problems arising from extreme cultural relativism)?

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