The coefficient of $x^{n}$ in the expansion of $(1 + x) {(1 - x)}^{n}$ is

{(- 1)}^{n - 1} n

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{(- 1)}^{n} (1 - n)

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{(- 1)}^{n - 1} {(n - 2)}^{2}

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(n - 1)

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Solution

The correct option is C ${(- 1)}^{n} (1 - n)$
We have
Coefficient of $x^{n}$ in $(1 + x) {(1 - x)}^{n}$
$=$ Coefficient of $x^{n}$ in ${(1 - x)}^{n}$ $+$ Coefficient of $x^{n - 1}$ in ${(1 - x)}^{n}$
$= {(- 1)}^{n} {^{n} C}_{n} + {(- 1)}^{n - 1} {^{n} C}_{n - 1} = {(- 1)}^{n} (1 - n)$

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