Freshman's Dream

Mistake
The freshman's dream is a name for the mistake:
 * $\left({x + y}\right)^n = x^n + y^n$

where $n$ is a real number.

The correct result is given by the Binomial Theorem.

Also see

 * Sophomore's Dream

Note the result given in Power of Sum Mod Prime, which is:
 * $\left({a + b}\right)^p \equiv a^p + b^p \pmod p$

where $p$ is a prime number.

This is also sometimes called the freshman's dream, but this one is in fact true.