Find the coefficient of x in the expansion of $(1 - 3 x + 7 x^{2}) (1 - x)^{16}$

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Solution

In the expansion of $E = (1 - x)^{16}$ , we have

$T_{r + 1} = (- 1)^{r} .^{16} C_{r} x^{r} .$

Product of given expression = $(1 - 3 x + 7 x^{2}) (1 - 16 x + . . .)$

Terms containing $x = [1 \times (- 16 x) + (- 3 x) \times 1] = (- 19 x) .$

$∴$ coefficient of x = $- 19$

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