Question

In the expansion of ${(3x+2)}^4$ the coefficient of middle term is:

• A. 36
• B. 216
• C. 54
• D. 81

Answer 1

Answer: (B)

In the expansion of ${(1+x)}^n,$ the middle term is $\frac{n}{2}th$ if $n$ is even and $\left(\frac{n}{2}+1\right)th$ if $n$ is odd.
In the given expansion ${(3x+2)}^4$
Here, $n=4$
$\therefore$ Middle term $=\frac{n}{2}+1,=\frac{4}{2}+1$
$=3$ rd term
$\therefore$ $T_3=T_{2+1}$
$={}^4{C}_2{(3x)}^2{(2)}^2$
The coefficient of middle term $={}^4{C}_2{3}^2{2}^2$
$=6\times 9\times 4=216$