Binomial theorem

The Binomial Theorem is a quick way (okay, it's a less slow way) of expanding (or multiplying out) a binomial expression that has been raised to some (generally inconveniently large) power. For instance, the expression (3x – 2)¹⁰ would be very painful to multiply out by hand. Thankfully, somebody figured out a formula for this expansion, and we can plug the binomial 3x – 2 and the power 10 into that formula to get that expanded (multiplied-out) form.

The formal expression of the Binomial Theorem is as follows:

$$ (x+y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k}y^k $$

Where,

$$ \binom{n}{k} = {n! \over k!(n-k)!} $$