Write down the values in the fifth row of Pascal’s triangle.

Hence or otherwise, find the term in \({x^3}\) in the expansion of \({(2x + 3)^5}\).

1, 5, 10, 10, 5, 1     A2     N2

[2 marks]

evidence of binomial expansion with binomial coefficient     (M1)

eg\(\,\,\,\,\,\)\(\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){a^{n - r}}{b^r}\), selecting correct term, \({(2x)^5}{(3)^0} + 5{(2x)^4}{(3)^1} + 10{(2x)^3}{(3)^2} +  \ldots \)

correct substitution into correct term     (A1)(A1)(A1)

eg\(\,\,\,\,\,\)\(10{(2)^3}{(3)^2},{\text{ }}\left( {\begin{array}{*{20}{c}} 5 \\ 3 \end{array}} \right){(2x)^3}{(3)^2}\)

Note: Award A1 for each factor.

\(720{x^3}\)     A1     N2

Notes: Do not award any marks if there is clear evidence of adding instead of multiplying.

Do not award final A1 for a final answer of 720, even if \(720{x^3}\) is seen previously.

[5 marks]