May/June 2026 Paper 13

Find the first four terms, in ascending powers of $x$, in the expansion of $(2+3x{)}^5$.

Hence, find the expansion up to and including the term in $x^3$ of $(1-3x)(2+3x{)}^5$.

Use your answer to 5(b), with a suitable value of $x$, to find an approximation to $0.97\times 2.03^5$. Write down your answer to 5 decimal places.