Răspuns:
[tex]a) \: a = 4 \sqrt{3} + 7 \sqrt{3} - 6 \sqrt{3} + 9 \sqrt{3} \\ a = 11 \sqrt{3} - 6 \sqrt{3} + 9 \sqrt{3 } = 5 \sqrt{3} + 9 \sqrt{3} = 14 \sqrt{3} [/tex]
[tex]c = 3 \sqrt{6} - \sqrt{15} + \sqrt{6} - 2 \sqrt{10} + \sqrt{15} + 2 \sqrt{10} \\ c = 4 \sqrt{6} [/tex]
[tex]b = 9 \sqrt{6} - 8 \sqrt{6} - 4 \sqrt{6} + \sqrt{6} \\ b = \sqrt{6} - 4 \sqrt{6} + \sqrt{6} = - 3\sqrt{6} + \sqrt{6} = - 2 \sqrt{6} [/tex]
[tex]a(b + c) = 14 \sqrt{3} \times ( - 2 \sqrt{6} + 4 \sqrt{6} ) = 14 \sqrt{3} \times 2 \sqrt{6} = 28 \sqrt{18} = 28 \sqrt{9 \times 2} = 28 \times 3 \sqrt{2} = 84 \sqrt{2} [/tex]
[tex]a \times b - a \times c = 14 \sqrt{3} \times ( - 2 \sqrt{6} ) - 14 \sqrt{3} \times 4 \sqrt{6} = - 28 \sqrt{18} - 56 \sqrt{18} = - 84 \sqrt{18} = - 84 \times 3 \sqrt{2} = - 252 \sqrt{2} [/tex]
[tex]b) \: a = 3 \sqrt{14} - 2 \sqrt{14} + 8 \sqrt{14} - 5 \sqrt{14} \\ a = 4 \sqrt{14} [/tex]
[tex]b = 2 \sqrt{15} - 12 \sqrt{15} + 3 \sqrt{15} + \sqrt{15} \\ b = - 6 \sqrt{15} [/tex]
[tex]c = \sqrt{15} - 4 \sqrt{15} + 2\sqrt{15} - 7 \sqrt{15} \\ c = - 8 \sqrt{15} [/tex]
[tex]a(b + c) = 4 \sqrt{14} \times ( - 6 \sqrt{15} - 8 \sqrt{15} ) = 4 \sqrt{14} \times ( - 14 \sqrt{15}) = - 56 \sqrt{210} [/tex]
[tex]a \times b - a \times c = 4 \sqrt{14} \times ( - 6 \sqrt{15} ) - 4 \sqrt{14} \times - 8 \sqrt{15} = - 24 \sqrt{210} + 32 \sqrt{210} = 8 \sqrt{210} [/tex]
