**This is in a textbook:**

CAUTION!

The area of a washer is

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.
John Smith…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…