# How do you use the binomial series to expand  (x-3)^5?

Mar 12, 2016

${x}^{5} - 15 {x}^{4} + 90 {x}^{3} - 270 {x}^{2} + 405 x - 243$.
${\left(a + b\right)}^{n} = {a}^{n} + n C 1 {a}^{n - 1} b + n C 2 {a}^{n - 2} {b}^{2} + . . n C n - r {a}^{n - r} {b}^{r} + \ldots + n C n {b}^{n}$
Here, a = x, b = $- 3$ and n = 5.
nCr = (n!)/(r!(n-r)!)