[tex]a) {( - 6 \sqrt{2} )}^{2} - {(5 \sqrt{3} })^{2} [/tex]
[tex] = ( { - 6})^{2} \times 2 + ( { - 5})^{2} \times 3[/tex]
[tex] = 36 \times 2 + 25 \times3[/tex]
[tex] = 72 + 75[/tex]
[tex] = 147[/tex]
[tex]b( {- 3 \sqrt{5} })^{2} + ({2 \sqrt{2}) }^{2} [/tex]
[tex] = ( { - 3})^{2} \times 5 + {2}^{2} \times 2[/tex]
[tex] = 9 \times 5+ 4 \times 2[/tex]
[tex] = 45 + 8[/tex]
[tex] = 53[/tex]
[tex]c) ({5 \sqrt{3} })^{2} - ({ - 2 \sqrt{27} })^{2} [/tex]
[tex] = {5}^{2} \times 3 - ( { - 2 \times 3 \sqrt{3} })^{2} [/tex]
[tex] = 25 \times 3 - ( { - 6 \sqrt{3} )}^{2} [/tex]
[tex] = 75 - (36 \times 3)[/tex]
[tex] = 75 - 108[/tex]
[tex] = - 33[/tex]
