This is in a textbook:

calculus caution

The area of a washer is pi*R^2-pi*r^2, which you can simplify to pi*(R^2-r^2), but not to pi*(R-r)^2. No matter how tempting it is to make the latter simplification, it’s wrong. Don’t do it.

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  1. …this isn’t a fail…expanding pi*(R-r)^2 gives you pi*(R^2-2Rr+r^2)=piR^2-2piRr+pir^2, and not pi*R^2-pi*r^2…

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