Expand and simplify ${\left( {{x^2} - \frac{2}{x}} \right)^4}$.

${\left( {{x^2} - \frac{2}{x}} \right)^4} = {({x^2})^4} + 4{({x^2})^3}\left( { - \frac{2}{x}} \right) + 6{({x^2})^2}{\left( { - \frac{2}{x}} \right)^2} + 4({x^2}){\left( { - \frac{2}{x}} \right)^3} + {\left( { - \frac{2}{x}} \right)^4}$     (M1)

$= {x^8} - 8{x^5} + 24{x^2} - \frac{{32}}{x} + \frac{{16}}{{{x^4}}}$     A3

Note: Deduct one A mark for each incorrect or omitted term.

[4 marks]

Most candidates solved this question correctly with most candidates who explained how they obtained their coefficients using Pascal’s triangle rather than the combination formula.