In a precision chemical synthesis, the concentration CCC, in moles per litre, of a specific reagent is modelled by the function C(x)=(12−4x)10C(x) = \left( \frac{1}{2} - 4x \right)^{10}C(x)=(21−4x)10 for 0≤x<0.1250 \le x < 0.1250≤x<0.125, where xxx represents the mass in grams of a stabilizer added.
Determine the first four terms, in ascending powers of xxx, of the binomial expansion of C(x)C(x)C(x). Give each coefficient as a simplified fraction or an integer.
