# Freshman's Dream

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## 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

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.