Question

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

• A. ${}^{6}C_3$
• B. $8\left({}^{6}C_3\right)$
• C. $8\left({}^{6}C_5\right)$
• D. ${}^{6}C_4$
• E. $8\left({}^{6}C_4\right)$

Answer 1

The correct option is B

$8\left({}^{6}C_3\right)$

Explanation for the correct answer:

We have to find the coefficient of middle term of the given expression.

Given expression is ${(x+2y)}^6$

The middle term of the given expression is $\frac{6}{2}+1=3+1=4$th term.

So, by binomial expansion,$T_4={}^{6}C_3{2}^3$

Therefore, the coefficient of $T_4=8{}^{6}C_3$

Hence, option(B) is correct answer.