a)
(3\sqrt2-4)(3\sqrt2+4)=9*2-16=18-16=2
b)
(3+2\sqrt5)(3-2\sqrt5)=9-4*5=9-20=-11
c)
(2+\sqrt3)^2(7-4\sqrt3)=(4+4\sqrt3+3)(7-4\sqrt3)=(7+4\sqrt3)(7-4\sqrt3)=47-16*3=49-48=1
d)
(2-2\sqrt2)^2(9+4\sqrt2)=(4-8\sqrt2+4*2)(9+4\sqrt2)=(12-8\sqrt2)(9+4\sqrt2)=
108+48\sqrt2-72\sqrt2-32*2=108-64-24\sqrt2=44-24\sqrt2
e)
(3+\sqrt7)^2-(3-\sqrt7)^2=9+6\sqrt7+7-(9-6\sqrt7+7)=16+6\sqrt7-9+6\sqrt7-7=16+12\sqrt7-16=12\sqrt7
f)
(2\sqrt2-\sqrt3)^2+(2\sqrt3+\sqrt2)^2=4*2-4\sqrt6+3+4*3+4\sqrt6+2=8+3+14=25