Find the constant term in the expansion of \({\left( {x - \frac{2}{x}} \right)^4}{\left( {{x^2} + \frac{2}{x}} \right)^3}\).

\({\left( {x - \frac{2}{x}} \right)^4} = {x^4} - 8{x^2} + 24 - \frac{{32}}{{{x^2}}} + \frac{{16}}{{{x^4}}}\)     (M1)(A1)

\({\left( {{x^2} + \frac{2}{x}} \right)^3} = {x^6} + 6{x^3} + 12 + \frac{8}{{{x^3}}}\)     (M1)(A1)

 Note: Accept unsimplified or uncalculated coefficients in the constant term

\( = 24 \times 12\)     (M1)(A1)

\( = 288\)     A1

[7 marks]

Many correct answers were seen, although most candidates used rather inefficient methods (e.g. expanding the brackets in multiple steps). In a very few cases candidates used the binomial theorem to obtain the answer quickly.