The 5 th term of the given expression is 330[tex](6x)^{7}( 6y)^{4}[/tex].
Step-by-step explanation:
Given,
[tex](6x+6y)^{11}[/tex]
To find the 5th term of the given expression.
Formula
In a binomial series [tex](a+b)^{n}[/tex], the r th term is = nC(r-1) [tex]a^{n-r-1} b^{r-1}[/tex], where,
nC(r-1) = [tex]\frac{n!}{(r-1)!(n-r+1)!}[/tex]
Now,
Putting, n=11, r = r, a=6x and b=6y we get,
5 th term = 11C4[tex](6x)^{7}( 6y)^{4}[/tex]
= [tex]\frac{11!}{4!7!}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]
= [tex]\frac{11X10X9X8X7!}{7!X4X3X2X1}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]
= 330[tex](6x)^{7}( 6y)^{4}[/tex]
Here is the answer.
