[tex]a)~~5\cdot (\sqrt{3} -4)+\sqrt{3} \cdot (6+2\sqrt{3} )=5\sqrt{3}-20+6\sqrt{3}+2\sqrt{3\cdot 3}=11\sqrt{3}-20+2\sqrt{9}=11\sqrt{3}-20+2\cdot 3=11\sqrt{3}-20+6=11\sqrt{3}-14\\\\b)~~2\sqrt{6} \cdot (2+5\sqrt{6})-3\cdot (5-4\sqrt{6})=4\sqrt{6}+10\sqrt{6\cdot 6}-15+12\sqrt{6}=4\sqrt{6}+10\sqrt{36}-15+12\sqrt{6}=16\sqrt{6}-15+10\cdot 6 =16\sqrt{6}-15+60=16\sqrt{6}+45\\\\[/tex]
[tex]c)~~4\sqrt{2}\cdot (5\sqrt{2}-6)+3\sqrt{2}\cdot (7-4\sqrt{2})=20\sqrt{2\cdot 2 }-24\sqrt{2}+21\sqrt{2}-12\sqrt{2\cdot 2}=20\sqrt{4}-3\sqrt{2}-12\sqrt{4}=20\cdot 2-3\sqrt{2}-12\cdot 2=40-3\sqrt{2}-24=16-3\sqrt{2}\\\\d)~~5\cdot (3+2\sqrt[3]{7} )-2\cdot (3\sqrt[3]{7}-4)=15+10\sqrt[3]{7}-6\sqrt[3]{7}+8=4\sqrt[3]{7}+23[/tex]
