Theorem
The binomial theorem says
\[(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^k y^{n-k}.\]Examples
We can use the binomial theorem to expand something like $(x + 5)^5$:
\[(x+5)^5 = \sum_{k = 0}^5 \binom{5}{k}x^k = x^5 + 25x^4 + 250x^3 + 1250x^2 + 3125x + 3125.\]