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∣<32 I(x) = \left(1 + \frac{2}{3}x\right)^{-3} \quad \text{for } |x| < \frac{3}{2} I(x)=(1+32x)−3for ∣x∣<23Find 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.
