Coeff of x in (1–2x3+3x5)(1+1x)8
= coeff of x in (1+1x)8+ coeff of x in (−2x3)(1+1x)8+ coeff of x in 3x5(1+1x)8
= coeff of x in (1+1x)8–2 coeff of x−2 in (1+1x)8+3 coeff of x−4 in (1+1x)8
rth term in (1+1x)8
$t_r = {^8C}_{r-1} ( \frac{1}{x})^{r-1} = {^8C_{r-1} x ^{1-r} $
For 1−r=1,r=0, coeff of x=0
For 1−r=−2,r=3, coeff of x=8C2
For 1−r=−4,r=5, coeff of x=8C4
Therefore
coeff of x=0−28C2+3×8C4
=154