How do you find the 5th term in the expansion of the binomial #(5a+6b)^5#?

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Answer 1 · 2017-10-14T11:09:25

#32400ab^4#

The fifth term descending a:

#5^1(5C4)a^1 6^4b^4= 5*5*1296a^1b^5=32400ab^4#

Answer 2 · 2017-10-18T00:10:31

#32400ab^4#

The expansion will have six terms starting with #a^5# and ending with #b^5#
Fifth term will be #5C(5-1)*a^(5-4)*b^4#

Given a as (5a) & b as (6b)

We also know #5C4 = 5C1 = 5#.

Substituting in the 5^th term, we get

#= 5*(5a)*(6b)^4 = 32400*a*b^4#