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.