Question

The coefficient of the middle term in the expansion of $(x+2y{)}^6$ is

• A. ${}^6{C}_3$
• B. $8{(}^6{C}_3)$
• C. $8{(}^6{C}_4)$
• D. ${}^6{C}_4$

Answer 1

Answer: (B)

Here, $n=6$ (even)
$\therefore$ The middle term in the given expansion is ${\left(\frac{6}{2}+1\right)}^{th}$ term $=4^{th}$ term
$\therefore T_4=T_{3+1}={}^6{C}_3{x}^{6-3}{\left(2y\right)}^3$
$={}^6{C}_3\times x^3\times 2^3\times y^3$
$={}^6{C}_3\times 8x^3{y}^3$
$\therefore$ Required coefficient is $8\left({}^6{C}_3\right)$.