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

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Answer 1 · 2017-11-21T17:12:26

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

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

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

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