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

Last Updated: 02.07.2025 15:52

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

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(n - 1)(n + 1)

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n^2 - n + n - 1

n^2 - 1

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Ive been pretending to be okay and acting as normal as possible, but Im actually completely heartbroken after a recent breakup. Its painful and really affecting me, to the point where I cant concentrate at work, Ive lost my appetite, I cant sleep, and It feels as if my whole world has been turned upside down. I loved him so much. He said so many cruel things to me and it made me realize he must not have loved me the way I loved him, or he wouldnt have said such horrible things. How do I handle the heartbreak and why cant I accept that he didnt love me and just forget about him?

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

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

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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

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Move the nub up to the top:

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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