Question

Find the 5th term of the expansion of ( 6x + 6y)^11

Answer 1

The 5 th term of the given expression is 330
`(6x)^(7)( 6y)^(4)`.

Explanation:

Given,

`(6x+6y)^(11)`

To find the 5th term of the given expression.

Formula

In a binomial series
`(a+b)^(n)`, the r th term is = nC(r-1)
`a^(n-r-1) b^(r-1)`, where,

nC(r-1) =
`(n!)/((r-1)!(n-r+1)!)`

Now,

Putting, n=11, r = r, a=6x and b=6y we get,

5 th term = 11C4
`(6x)^(7)( 6y)^(4)`

=
`(11!)/(4!7!)`
`(6x)^(7)( 6y)^(4)`

=
`(11X10X9X8X7!)/(7!X4X3X2X1)`
`(6x)^(7)( 6y)^(4)`

= 330
`(6x)^(7)( 6y)^(4)`

Here is the answer.