[tex]a)( \sqrt{27} - 4)(3 \sqrt{3} + 4)[/tex]
[tex] = (3 \sqrt{3} - 4)(3 \sqrt{3} + 4)[/tex]
[tex] = {(3 \sqrt{3}) }^{2} - {4}^{2} [/tex]
[tex] = 27 - 16[/tex]
[tex] = 11[/tex]
[tex]b) {( \sqrt{2} + 1) }^{2} + 2 \sqrt{8} [/tex]
[tex] = {( \sqrt{2}) }^{2} + 2 \times \sqrt{2} \times 1 + {1}^{2}+2 \times 2 \sqrt{2} [/tex]
[tex] = 2 + 2 \sqrt{2} +1 + 4 \sqrt{2} [/tex]
[tex] = 6 \sqrt{2} + 3[/tex]
[tex] = 3(2 \sqrt{2} + 1)[/tex]
[tex]c) {( \sqrt{5} - 2)}^{2} + 4( \sqrt{5} - 1)[/tex]
[tex] = {( \sqrt{5}) }^{2} - 2 \times \sqrt{5} \times 2 + {2}^{2} + 4 \sqrt{5} - 4[/tex]
[tex] = 5 - 4 \sqrt{5} + 4 + 4 \sqrt{5} - 4[/tex]
[tex] = 5 + 4 \sqrt{5} - 4 \sqrt{5} + 4 - 4[/tex]
[tex] = 5[/tex]
