(2 \sqrt{2} - \sqrt{2} )^2=(2 \sqrt{2})^2-2*2\sqrt{2}*\sqrt{2}+(\sqrt{2} )^2=4*2-4*2+2=2
(2 \sqrt{2} -4) (2 \sqrt{2} +4) =(2 \sqrt{2})^2-4^2=4*2-16=8-16=-8
(4 \sqrt{3} + 5\sqrt{2} )^2 = (4 \sqrt{3}) ^2+2*4 \sqrt{3}*5\sqrt{2}+(5\sqrt{2} )^2=
=16*3 +40\sqrt{3*2}+25*2=48+40\sqrt{6} +50 =98+40\sqrt{6}
(3\sqrt{5} +7)(3\sqrt{5} -7) =(3\sqrt{5})^2-7^2=9*5-49=45-49=-4