Q. The coefficient of the middle term in the expansion of ${(x + 2y)}^{6}$ is
A) $\ ^{6}C_{3}$
B) $8(\ ^{6}C_{3})$
C) $8(^{6}C_{5})$
D) $\ ^{6}C_{4}$
Explanation
(b)
In the expansion of $(x + 2y)^{6},$
$\left( \frac{6}{2} + 1 \right)th\ term\ is\ the\ middle\ term.$
$\therefore\ \ \ \ \ T_{4} = T_{3 + 1} = \ ^{6}C_{3}x^{6 - 3}(2y)^{3}$
$= \ \ \ \ 8\left( \ ^{6}C_{3} \right)(xy)^{3}$
$\therefore$ Coefficient of middle term
$\ \ \ \ \ \ \ \ \ \ \ \ \ = 8(\ ^{6}C_{3})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.