Question

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

Answer 1

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

Step-by-step 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) = $\frac{n!}{(r-1)!(n-r+1)!}$

Now,

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

5 th term = 11C4$(6x)^{7}( 6y)^{4}$

= $\frac{11!}{4!7!}$$(6x)^{7}( 6y)^{4}$

= $\frac{11X10X9X8X7!}{7!X4X3X2X1}$$(6x)^{7}( 6y)^{4}$

= 330$(6x)^{7}( 6y)^{4}$

Here is the answer.