CAIE A-Level Mathematics AS 1.6.1 Binomial Expansion Questions

$x^{5}+10 x^{3}+40 x+\frac{80}{x}+\frac{80}{x^{3}}+\frac{32}{x^{5}}$ or $x^{5}+10 x^{3}+40 x+80 x^{-1}+80 x^{-3}+32 x^{-5}$

B2, 1, 0

B2, all terms correct, B1 5 terms correct. Terms must be simplified. Lists of terms allowed.

their $40 \times a+\left(\right.$ their coefficient of $\left.x^{-1}\right) \times b=0$
Coefficients of a and b must be non-zero, allow x 's so
long as they are dealt with correctly.

(their coefficient of $\left.x^{-1}\right) \times a+\left(\right.$ their coefficient of $\left.x^{-3}\right) \times b=80$
Coefficients of a and b must be non-zero, allow x 's as
long as they are dealt with correctly.

$a=2 \quad b=-1$
Dependent on both M marks, may be seen without working.