Question

find the 6th term in the expansion of (3x + y/2) ^9​

Answer 1

Answer:

3x X 9 + y/9 X 9 might be the right answer but the exact answer ‍♀

Answer 2

The 6th term in the expansion of $(3x+\frac{y}{2} )^{9}$  is  $330.75\ x^{4}\ y^{5}$ .

Step-by-step explanation:

Given:

Expression $(3x+\frac{y}{2} )^{9}$ .

To Find:

The 6th term in the expansion of $(3x+\frac{y}{2} )^{9}$.

Formula Used:

$(p+q)^{n} = nC0\ p^{n} +nC1 \ p^{n-1} \ q+ ........... + nCn \ y^{n}$

General Term Binomial expression $= Tr+1 = nCr\ x^{n-r} \ q^{r}$ ----formula no.01

Solution:

As given- Expression $(3x+\frac{y}{2} )^{9}$

Applying formula no.01.

$p=3x$        and  $q=\frac{y}{2}$

$6^{th}$ term of Binomial expression  $= T(5+1) = 9C5\ (3x)^{9-5} \ (\frac{y}{2} )^{5}$

                                                                          $= 9C5\ (3x)^{4} \ (\frac{y}{2} )^{5}$

                                                                          $= \frac{9!}{(9-5)!\ 5!} \ (81 x^{4} ) (\frac{y^{5} }{32} )$

                                                                         $= \frac{9!}{4!\ 5!} \ (81 x^{4} ) (\frac{y^{5} }{32} )$

                                                                        $= \frac{9!}{4!\ 5!} \ (\frac{84}{32}) x^{4} \ y^{5}$

                                                                         $= 330.75\ x^{4}\ y^{5}$

                                                                         

Thus,the $6^{th}$  term in the expansion of   $(3x+\frac{y}{2} )^{9}$   is $330.75\ x^{4}\ y^{5}$ .