Write down and simplify the expansion of ${(2 + x)^4}$ in ascending powers of $x$.

Hence find the exact value of ${(2.1)^4}$.

${(2 + x)^4} = {2^4} + 4 \bullet {2^3}x + 6 \bullet {2^2}{x^2} + 4 \bullet 2{x^3} + {x^4}$     M1(A1)

Note:     Award M1 for an expansion, by whatever method, giving five terms in any order.

$= 16 + 32x + 24{x^2} + 8{x^3} + {x^4}$     A1

Note:     Award M1A1A0 for correct expansion not given in ascending powers of $x$.

[3 marks]

let $x = 0.1$ (in the binomial expansion)     (M1)

${2.1^4} = 16 + 3.2 + 0.24 + 0.008 + 0.0001$     (A1)

$= 19.4481$     A1

Note:     At most one of the marks can be implied.

[3 marks]

Total [6 marks]