Question

Expand the following binomial:
${(\frac{1}{2}+a)}^8$

Answer 1

$=\frac{(1+2a{)}^8}{2^8}$

$(1+8.(2a)+\frac{8.7}{2}(2a{)}^2+\frac{\mathrm{8.7.6}}{3!}(2a{)}^3+\frac{\mathrm{8.7.6.5}}{4!}(2a{)}^4+\frac{\mathrm{8.7.6.5.4}}{5!}(2a{)}^5+\frac{\mathrm{8.7.6.5.4.3}}{6!}(2a{)}^6+$

$\frac{\mathrm{8.7.6.5.4.3.2}}{7!}(2a{)}^7+1.(2a{)}^8)\frac{1}{2^8}$