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Q.
The coefficient of the middle term in the expansion of $(x + 2y)^6$ is
Binomial Theorem
Solution:
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 $8\left(^{6}C_{3}\right)$.