Binomial Expansions

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

General Term

$T_{r+1}=\dbinom{n}{r}a^{n-r} b^r$

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