[tex](2 \sqrt{3} + 3 \sqrt{5} )(2 \sqrt{3} - 3 \sqrt{5} ) = (2 \sqrt{3} ) {}^{2} - {(3 \sqrt{5}) }^{2} = 4 \times 3 - 9 \times 5 = 12 - 45 = - 33[/tex]