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

$\begin{array}{1 1}(A)\;19\\(B)\;-19\\(C)\;18\\(D)\;-48\end{array}$

Toolbox:
• $T_{r+1}=nC_ra^{n-r}b^r$
$(1-3x+7x^2)(1-x)^{16}$
$\Rightarrow (1-3x+7x^2)[16C_0x^0-16C_1x+16C_2x^2......+16C_{n-1}(-1)^{n-1}x^{n-1}+nC_n(-1)6nx^n]$
$\Rightarrow (1-3x+7x^2)[1-16C_1x+16C_2x^2+16C_3x^3+16C_4x^4+16C_5x^5+......16C_{16}x^{16}]$
$\Rightarrow -3.16C_1$
$\Rightarrow -3\times \large\frac{16!}{1!15!}$
$\Rightarrow -3\times 16$
$\Rightarrow -48$
Hence (D) is the correct answer.