Explicação passo-a-passo:
[tex]a)2 \sqrt{3} .( \sqrt{12} + \sqrt{3} ) = 2 \sqrt{3.12} + 2 \sqrt{3.3} = 2 \sqrt{36} + 2 \sqrt{9} = 2 \times 6 + 2 \times 3 = 12 + 6 = 18[/tex]
[tex]b)(2 + \sqrt{3} ).(3 - \sqrt{3} ) = 2.3 - 2 \sqrt{3} + 3 \sqrt{3} - ( \sqrt{3} ) {}^{2} = [/tex]
[tex]6 - 2 \sqrt{3} + 3 \sqrt{3} - 3 = 3 + \sqrt{3} [/7tex]
[tex](2 \sqrt{5} + \sqrt{7} ).( \sqrt{5} - 2 \sqrt{7} ) = 2( \sqrt{5} ) {}^{2} - 4 \sqrt{35} + 7 \sqrt{35} - 2( \sqrt{7} ) {}^{2} = 10 + 11 \sqrt{35} - 14 = [/tex]
[tex]11 \sqrt{35} - 4[/tex]
[tex]( \sqrt{2} + \sqrt{3} ).(2 - \sqrt{3} ) = 2 \sqrt{2} - \sqrt{6} - 3 = [/tex]