## Caution!

Posted by mathfail
on April 3, 2010
**This is in a textbook:**

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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…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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