Question:
Find the coefficient of $x$ in the expansion of $\left(1-3 x+7 x^{2}\right)(1-x)^{16}$
Solution:
Given $\left(3 x-\frac{2}{x^{2}}\right)^{15}$
$=\left(1-3 x+7 x^{2}\right)\left({ }^{16} C_{0}-{ }^{16} C_{1} x^{1}+{ }^{16} C_{2} x^{2}+\ldots+{ }^{16} C_{16} x^{16}\right)$
$=\left(1-3 x+7 x^{2}\right)\left(1-16 x+120 x^{2}+\ldots\right)$
Coefficient of $x=-19$
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