use binomial
$(x^3) \underbrace{(1+2x)^{-2}}$
find coefficient of $(x^9)$ from 2nd term
it will be : $\frac{n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8) \times (2x)^{9}}{9!}$
n = -2 here
$\frac{-2(-3)(-4)(-5)(-6)(-7)(-8)(-9)(-10) \times (2x)^{9}}{9!}$
=$- \frac{2(3)(4)(5)(6)(7)(8)(9)(10) \times (2x)^{9}}{9\times 8!}$
= $10(-1) \times 512 x^{9} = -5120$