A researcher models the intensity I I\,I of a signal as it penetrates a specific material of thickness x x\,x cm. The model is given by I(x)=(1+23x)−3for ∣x∣<32I(x) = \left(1 + \frac{2}{3}x\right)^{-3} \quad \text{for } |x| < \frac{3}{2}I(x)=(1+32x)−3for ∣x∣<23
Find the binomial expansion of I(x)I(x)I(x) in ascending powers of x x\,x up to and including the term in x3x^3x3. Simplify each coefficient fully and present them as exact fractions.
Practise Edexcel A Level Maths 4.2 Expanding (a + bx)^n with exam-style questions for A Level Maths. 99 questions, 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.