Find the term ${x^3}$ in the expansion of ${\left( {\frac{2}{3}x - 3} \right)^8}$ .

evidence of using binomial expansion     (M1)

e.g. selecting correct term, ${a^8}{b^0} + \left( {\begin{array}{*{20}{c}} 8\\ 1 \end{array}} \right){a^7}b + \left( {\begin{array}{*{20}{c}} 8\\ 2 \end{array}} \right){a^6}{b^2} + \ldots$

evidence of calculating the factors, in any order     A1A1A1

e.g. 56 , $\frac{{{2^2}}}{{{3^3}}}$ , $- {3^5}$ , $\left( {\begin{array}{*{20}{c}} 8\\ 5 \end{array}} \right){\left( {\frac{2}{3}x} \right)^3}{( - 3)^5}$

$- 4032{x^3}$ (accept = $- 4030{x^3}$ to 3 s.f.)     A1     N2

[5 marks]

Candidates produced mixed results in this question. Many showed a binomial expansion in some form, although simply writing rows of Pascal’s triangle is insufficient evidence. A common error was to answer with the coefficient of the term, and many neglected the use of brackets when showing working. Although sloppy notation was not penalized if candidates achieved a correct result, for some the missing brackets led to a wrong answer.