A mistake
often made by first year calculus students is in thinking that

(*a*+*b*)^{n}^{ }= *a ^{n}* +

A related result (that is true) known as the the “Freshman’s Dream Theorem” is that

(*a*+*b*)^{n}^{ }= *a ^{n}* +

Source:
Pratibha Ghatage and Brian Scott, When is (*a*+*b*)^{n}^{ }= *a ^{n}* +

Also
see: http://en.wikipedia.org/wiki/Carmichael_number

If
there was a calculus “Professor’s Dream” it would likely be that all students
carefully read (and then read again several more times) the following pages *before* they reach calculus:

Paul's Online Math Notes: Common
Math Errors

http://tutorial.math.lamar.edu/extras/commonerrors/commonmatherrors.aspx

The Most Common Errors in Undergraduate Mathematics

http://www.math.vanderbilt.edu/~schectex/commerrs/