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  4. The coefficient of x6 in the expansion of (1 - x)8(1 + x)12 is equal to

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Q. The coefficient of $x^{6}$ in the expansion of $\left(1 - x\right)^{8}\left(1 + x\right)^{12}$ is equal to

NTA AbhyasNTA Abhyas 2020Binomial Theorem

Solution:

$\left(1 - x\right)^{8}\left(1 + x\right)^{12}=\left(1 - x^{2}\right)^{8}\left(1 + x\right)^{4}$
$=\left(1 - 8 x^{2} + 28 x^{4} - 56 x^{6} + \ldots \right)\left(1 + 4 x + 6 x^{2} + 4 x^{3} + x^{4}\right)$
Hence, the coefficient of $x^{6}=-8+168-56=160=104$