The population density ρ(r)\rho(r)ρ(r) of a certain bacterial colony as a function of the distance r r\,r from its center is modeled by the function ρ(r)=(3+2r)−3\rho(r) = (3 + 2r)^{-3}ρ(r)=(3+2r)−3 for ∣r∣<1.5|r| < 1.5∣r∣<1.5.
Find the binomial expansion of ρ(r)\rho(r)ρ(r) in ascending powers of r r\,r up to and including the term in r3r^3r3, fully simplifying each coefficient.
