Binomial Expansions
Binomial Expansions
$(a+b)^n = a^n + \dbinom{n}{1}a^{n-1} b + \dbinom{n}{2}a^{n-2} b^2 + … $
$+ \dbinom{n}{r}a^{n-r} b^r + … + b^{n}$
$+ \dbinom{n}{r}a^{n-r} b^r + … + b^{n}$
General Term
$T_{r+1}=\dbinom{n}{r}a^{n-r} b^r$
$n$ choose $r$
$\dbinom{n}{r}=\dfrac{n!}{r!(n-r)!} = \dfrac{n(n-1)…(n-r+1)}{r!}$
