a)  $5\left(\sqrt{3}-4\right)+\sqrt{3}\left(6+2\sqrt{3}\right)=5\cdot \sqrt{3}-5\cdot 4+\sqrt{3}\cdot 6+\sqrt{3}\cdot 2\sqrt{3}=$  

$5\sqrt{3}-20+6\sqrt{3}+2\cdot 3=5\sqrt{3}-20+6\sqrt{3}+6=11\sqrt{3}-14$  

---

b)  $2\sqrt{6}\left(2+5\sqrt{6}\right)-3\left(5-4\sqrt{6}\right)=2\sqrt{6}\cdot 2+2\sqrt{6}\cdot 5\sqrt{6}-3\cdot 5+3\cdot 4\sqrt{6}=$  

$=4\sqrt{6}+10\cdot 6-15+12\sqrt{6}=4\sqrt{6}+60-15+12\sqrt{6}=16\sqrt{6}+45$  

---

c)  $4\sqrt{2}\left(5\sqrt{2}-6\right)+3\sqrt{2}\left(7-4\sqrt{2}\right)=4\sqrt{2}\cdot 5\sqrt{2}-4\sqrt{2}\cdot 6+3\sqrt{2}\cdot 7-3\sqrt{2}\cdot 4\sqrt{2}=$  

$4\cdot 5\cdot 2-24\sqrt{2}+21\sqrt{2}-3\cdot 4\cdot 2=40-24\sqrt{2}+21\sqrt{2}-24=16-3\sqrt{2}$

---

d)  $5\left(3+2\sqrt[3]{7}\right)-2\left(3\sqrt[3]{7}-4\right)=5\cdot 3+5\cdot 2\sqrt[3]{7}-2\cdot 3\sqrt[3]{7}+2\cdot 4=15+10\sqrt[3]{7}-6\sqrt[3]{7}+8=23+4\sqrt[3]{7}$