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.
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.