[tex](a+b)(c+d) = ac + ad + bc + bd\\\\(a-b)(a+b) = a^{2}-b^{2}[/tex]
[tex]a) \ (3-\sqrt{2})(\sqrt{2}-1) = 3\sqrt{2}-3-2+\sqrt{2} = 4\sqrt{2}-5\\\\\\b) \ \sqrt{3}-(\sqrt{3}-5)(4+\sqrt{3}) = \sqrt{3}-(4\sqrt{3}+3-20-5\sqrt{3})=\sqrt{3}-(-17-\sqrt{3})=\\\\=\sqrt{3}+17+\sqrt{3}=17+2\sqrt{3}[/tex]
[tex]c) \ (\sqrt{5}-1)(\sqrt{5}+1) = (\sqrt{5})^{2}-1^{2} = 5-1 = 4\\\\\\d) \ (\sqrt{3}-2)(5+\sqrt{2})-\sqrt{6} =5\sqrt{3}+\sqrt{6}-10-2\sqrt{2}-\sqrt{6} = 5\sqrt{3}-2\sqrt{2}-10[/tex]
