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

Last Updated: 28.06.2025 08:40

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

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Do all vehicles, including cars and SUVs, need to be lifted up on ramps in order to change the oil filter? If not, what is an alternative method for changing the oil filter without lifting the vehicle?

Move the nub up to the top:

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

n^2 - n + n - 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

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

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

(n - 1)(n + 1)

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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

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n^2 - 1