How do you find the fifth term of (a-3)^8(a3)8?

1 Answer
Nov 21, 2017

56x^3(-3)^5=-13,606x^356x3(3)5=13,606x3

Explanation:

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

((n),(k)) 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

56x^3(-3)^5=-13,606x^3