$a)(1+2\sqrt{3}-\sqrt{2}).(1+2\sqrt{3}+\sqrt{2})_{}$
$=(1+2\sqrt{3})^2-2_{}$
$=1+4\sqrt{3}+12-2_{}$
$=11+4\sqrt{3}_{}$
$b)_{}$ $(1-\sqrt{3})^2.(1+2\sqrt{3})^2_{}$
$=[(1-\sqrt{3}).(1+2\sqrt{3}) ]^2_{}$
$=(1+2\sqrt{3}-\sqrt{3}-6)^2_{}$
$=(-5+\sqrt{3})^2_{}$
$=(\sqrt{3}-5)^2_{}$
$=3-10\sqrt{3}+25_{}$
$=28-10\sqrt{3}_{}$