[tex]a)(2 + \sqrt{3})(1 + \sqrt{3} ) = 2 + 2 \sqrt{3} + \sqrt{3} + 3 = 5 + 3 \sqrt{3} [/tex]
[tex]b)(3 - \sqrt{5} )( \sqrt{5} + 2) = 3 \sqrt{5} + 6 - 5 - 2 \sqrt{5} = 1 + \sqrt{5} [/tex]
[tex]c)4(5 \sqrt{2} - 6) + (1 + \sqrt{2} )(2 + \sqrt{2} ) = 20 \sqrt{2} - 24 + 2 + \sqrt{2} + 2 \sqrt{2} + 2 = - 20 + 23 \sqrt{2} [/tex]
[tex]d) - 3(2 \sqrt{7} + 3) - (4 - \sqrt{7} )(3 \sqrt{7} + 1) = - 6 \sqrt{7} - 9 - (12 \sqrt{7} + 4 - 21 - \sqrt{7} ) = - 6 \sqrt{7} - 9 - (11 \sqrt{7} - 17) = - 6 \sqrt{7} - 9 - 11 \sqrt{7} + 17 = 8 - 17 \sqrt{7} [/tex]
