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The middle term in the expansion of ${(1 + 3 x + 3 x^{2} + x^{3})}^{50}$ is

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$156 x^{156}$

$149 x$

$150 c_{75} . x^{75}$

none

answer is C.

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Detailed Solution

$\begin{array}{l} {[{(1 + x)}^{3}]}^{50} = {(1 + x)}^{150} \\ n = 150, n i s e v e n \\ t h e n m i d d l e t e r m i s T_{\frac{n}{2} + 1} \\ = 150 c_{75} . x^{75} \end{array}$

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