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#