Find the term independent of \(x\) in the binomial expansion of \({\left( {2{x^2} + \frac{1}{{2{x^3}}}} \right)^{10}}\).

attempt at binomial expansion, relevant row of Pascal’s triangle or use of general term with binomial coefficient must be seen     (M1)

term independent of \(x\) is \(\left( {\begin{array}{*{20}{c}}{10} \\4\end{array}} \right){(2{x^2})^6}{\left( {\frac{1}{{2{x^3}}}} \right)^4}\) (or equivalent)     (A1)(A1)(A1)

Notes:     \(x\)’s may be omitted. Also accept \(\left( {\begin{array}{*{20}{c}}{10} \\6\end{array}} \right)\) or 210.

\( = 840\)     A1

[5 marks]