[tex]a) \ (\sqrt{3}+2\sqrt{2})(4\sqrt{3}-8\sqrt{2}) =\sqrt{3}\cdot4\sqrt{3}+2\sqrt{2}\cdot(-8\sqrt{2})+2\sqrt{2}\cdot4\sqrt{3} + 2\sqrt{2}\cdot(-8\sqrt{2})=\\\\=3\cdot4 -16\cdot2 +8\sqrt{2\cdot3}-16\cdot2 = 12-32+8\sqrt{6}-32 = 8\sqrt{6}-52[/tex]
[tex]b) \ (2\sqrt{5}-4\sqrt{2})(2\sqrt{2}+\sqrt{5}) =2\sqrt{5}\cdot2\sqrt{2}+2\sqrt{5}\cdot\sqrt{5}-4\sqrt{2}\cdot2\sqrt{2} -4\sqrt{2}\cdot\sqrt{5} =\\\\=4\sqrt{5\cdot2} +2\cdot5 -8\cdot2 - 4\sqrt{2\cdot5} = 4\sqrt{10} + 10-16-4\sqrt{10} = -6[/tex]
