Binomial Expansions

Binomial Expansion

$(a+b)^n = a^n + \dbinom{n}{1}a^{n-1} b + \dbinom{n}{2}a^{n-2} b^2 + \ldots + \dbinom{n}{r}a^{n-r} b^r + \ldots + b^{n}$

General Term

$\dbinom{n}{r}a^{n-r} b^r$

$n$ Choose $r$

$\dbinom{n}{r}=\dfrac{n!}{r!(n-r)!} = \dfrac{n(n-1)\ldots(n-r+1)}{r!}$