Expand ${(2 - 3x)^5}$ in ascending powers of x, simplifying coefficients.

clear attempt at binomial expansion for exponent 5     M1

${2^5} + 5 \times {2^4} \times ( - 3x) + \frac{{5 \times 4}}{2} \times {2^3} \times {( - 3x)^2} + \frac{{5 \times 4 \times 3}}{6} \times {2^2} \times {( - 3x)^3}$

$+ \frac{{5 \times 4 \times 3 \times 2}}{{24}} \times 2 \times {( - 3x)^4} + {( - 3x)^5}$     (A1)

Note: Only award M1 if binomial coefficients are seen.

$= 32 - 240x + 720{x^2} - 1080{x^3} + 810{x^4} - 243{x^5}$     A2

Note: Award A1 for correct moduli of coefficients and powers. A1 for correct signs.

Total [4 marks]

Generally well done. The majority of candidates obtained a quintic with correct alternating signs. A few candidates made arithmetic errors. A small number of candidates multiplied out the linear expression, often correctly.