Expand \({(x - 2)^4}\) and simplify your result.

Find the term in \({x^3}\) in \((3x + 4){(x - 2)^4}\) .

evidence of expanding     M1

e.g. \({(x - 2)^4} = {x^4} + 4{x^3}( - 2) + 6{x^2}{( - 2)^2} + 4x{( - 2)^3} + {( - 2)^4}\)     A2     N2

\({(x - 2)^4} = {x^4} - 8{x^3} + 24{x^2} - 32x + 16\)

[3 marks]

finding coefficients, \(3 \times 24( = 72)\) , \(4 \times( - 8)( = - 32)\)     (A1)(A1)

term is \(40{x^3}\)     A1     N3

[3 marks]

Where candidates recognized the binomial nature of the expression, many completed the expansion successfully, although some omitted the negative signs.

Where candidates recognized the binomial nature of the expression, many completed the expansion successfully, although some omitted the negative signs. Few recognized that only the multiplications that achieve an index of 3 are required in part (b) and distributed over the entire expression. Others did not recognize that two terms in the expansion must be combined.