May/June 2026 Paper 12

Find the first three terms, in ascending powers of $x$, in the expansion of ${\left(3-\frac{1}{2}x\right)}^4$.

Find the first three terms, in ascending powers of $x$, in the expansion of $(2+ax{)}^3$. Give your answer in terms of the constant $a$.

It is now given that the coefficient of $x^2$ in the expansion of ${\left(3-\frac{1}{2}x\right)}^4(2+ax{)}^3$ is $-108$. Find the value of $a$.