How do you find the fifth term of (a-3)^8?

Nov 21, 2017

$56 {x}^{3} {\left(- 3\right)}^{5} = - 13 , 606 {x}^{3}$

Explanation:

Use the Binomial Theorm. The fifth term (or any numbered term) can be found with the following formula:

$\left(\begin{matrix}n \\ k\end{matrix}\right) {a}^{n - k} {b}^{k}$ where $a = x$ and $b = - 3$

The coefficient is

((n),(k)) = (n!)/((n-k)!k!)

where $n = 8$ and $k = 5$ (because we want the 5th term)

((8),(5)) = (8!)/((8-5)!5!)=(8!)/(3!5!)=(8*7*6*cancel(5!))/(3!cancel(5!))=56

So the 5th term is

$56 {x}^{3} {\left(- 3\right)}^{5} = - 13 , 606 {x}^{3}$