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

Hence, find the term in \({x^2}\) in \({(2 + x)^4}\left( {1 + \frac{1}{{{x^2}}}} \right)\) .

evidence of expanding     M1

e.g. \({2^4} + 4({2^3})x + 6({2^2}){x^2} + 4(2){x^3} + {x^4}\) , \((4 + 4x + {x^2})(4 + 4x + {x^2})\)

\({(2 + x)^4} = 16 + 32x + 24{x^2} + 8{x^3} + {x^4}\)     A2     N2

[3 marks]

finding coefficients 24 and 1     (A1)(A1)

term is \(25{x^2}\)     A1     N3

[3 marks]

Surprisingly few candidates employed the binomial theorem, choosing instead to expand by repeated use of the distributive property. This earned full marks if done correctly, but often proved prone to error.

Candidates often expanded the entire expression in part (b). Few recognized that only two distributions are required to answer the question. Some gave the coefficient as the final answer.