Question

in expansion of (3x+2)^4,coefficient of middle term is a)36 b)54 c)81 d)216​

Answer 1

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Answer 2

Answer:

$\display \sf{{\rightarrow 216}}$

Step-by-step explanation:

$\display \text{{Given expansion as :}}$

$\display \sf{{(3x+2)^4}}$

$\display \text{{Since power is even}}\\\\\\\display \text{{Middle term = \sf \dfrac{n}{2} +1 }}$

= > 4 / 2 + 1

= > 3

So we get r = 3

Now :

$\display \sf{{T_{r+1} =\ ^nC_r \ a^{n-r} \ b^r}}\\\\\\\display \sf{{T_{2+1} =\ ^4C_2 \ (3x)^{4-2} \ (2^2)}}\\\\\\\display \sf{{T_{3} =\ ^4C_2 \ (3x)^{2} \ (4)}}\\\\\\\display \sf{{\rightarrow \dfrac{4!\times9x^2\times4}{(4-2)!\times2!} }}\\\\\\\display \sf{{\rightarrow 24\times9x^2}}\\\\\\\display \sf{{\rightarrow 216 x^2}}$

$\display \text {{Therefore middle term of expansion is 216.}}$