Odpowiedź:
[tex]a)\ \ 5(\sqrt{3}-4)+\sqrt{3}(6+2\sqrt{3})=5\sqrt{3}-5\cdot4+6\sqrt{3}+\sqrt{3}\cdot2\sqrt{3}=\\\\=5\sqrt{3}-20+6\sqrt{3}+2\sqrt{3\cdot3}=11\sqrt{3}-20+2\cdot3= 11\sqrt{3}-20+6=11\sqrt{3}-14\\\\\\b)\ \ 2\sqrt{6}(2+5\sqrt{6})-3(5-4\sqrt{6})=2\sqrt{6}\cdot2+2\sqrt{6}\cdot5\sqrt{6}-3\cdot5-3\cdot(-4\sqrt{6})=\\\\=4\sqrt{6}+10\sqrt{6\cdot6}-15+12\sqrt{6}=4\sqrt{6}+10\cdot6-15+12\sqrt{6}=16\sqrt{6}+60-15=\\\\=16\sqrt{6}+45[/tex]
[tex]c)\ \ 4\sqrt{2}(5\sqrt{2}-6)+3\sqrt{2}(7-4\sqrt{2})=4\sqrt{2}\cdot5\sqrt{2}-4\sqrt{2}\cdot6+3\sqrt{2}\cdot7-3\sqrt{2}\cdot4\sqrt{2}=\\\\=20\sqrt{2\cdot2}-24\sqrt{2}+21\sqrt{2}-12\sqrt{2\cdot2}=20\cdot2-3\sqrt{2}-12\cdot2=\\\\=40-3\sqrt{2}-24=16-3\sqrt{2}[/tex]
[tex]d)\ \ 5(3+2\sqrt[3]{7})-2(3\sqrt[3]{7}-4)=5\cdot3+5\cdot2\sqrt[3]{7}-2\cdot3\sqrt[3]{7}-2\cdot(-4)=\\\\=15+10\sqrt[3]{7}-6\sqrt[3]{7}+8=23+4\sqrt[3]{7}[/tex]
