Find the constant term in the expansion of \({\left( {4{x^2} - \frac{3}{{2x}}} \right)^{12}}\).

attempting a valid method to obtain the required term in the expansion     (M1)

Note: Valid methods include an attempt to expand, noting the behaviour of the powers of \(x\), use of the general binomial expansion term, use of a ratio etc.

identifying the correct term     (A1)

\(\left( {\begin{array}{*{20}{c}} {12} \\ 8 \end{array}} \right) \times {4^4} \times {\left( { - \frac{3}{2}} \right)^8}{\text{ }}\left( { = 495 \times {4^4} \times {{\left( { - \frac{3}{2}} \right)}^8}} \right)\)    M1A1

Note: Accept \(\left( {\begin{array}{*{20}{c}} {12} \\ 4 \end{array}} \right)\).

Note: Award M1 for the product of a binomial coefficient, a power of 4 and either a power of \( - \frac{3}{2}\) or \(\frac{3}{2}\).

\( = 3\,247\,695\)    A1

[5 marks]