Problem

(a) Expand $\left(2-\frac{1}{2}x\right)^6$ in ascending powers of $x$ up to and including the term in $x^3$.

(b) Hence find the coefficient of $x^3$ in the expansion of $\left(3-x+2x^3\right)\left(2-\frac{1}{2}x\right)^6$.