Math Question (abstract)?

Okay, so I was doing a little bit of fooling around with math and formulas and algebra 'n' stuff, and I discovered this.

(n·n) - n

seemingly equals

n · (n-1)

They both give the same answer, no matter what integer you substitute for n. Why is this the case? Is it truly the case? How does it work?

Thanks,

Aristides

Update:

but how does n*n - n * 1 become n * (n-1)

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