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 known as

Some sources cite this as the child's binomial theorem.

Also see

• Sophomore's Dream

Note the result given in Power of Sum Modulo 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.