Freshman's Dream

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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.