Simplify each of the following expressions:
$(i)$ $(3+\sqrt{3})(2+\sqrt{2})$
$(ii)$ $(3+\sqrt{3})(3-\sqrt{3})$
$(iii)$ $(\sqrt{5}+\sqrt{2})^{2}$
$(iv)$ $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$

(N/A) $(i)$ $(3+\sqrt{3})(2+\sqrt{2}) = 3(2+\sqrt{2}) + \sqrt{3}(2+\sqrt{2})$
$= 6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6}$
$(ii)$ Using the identity $(a+b)(a-b) = a^2 - b^2$:
$(3+\sqrt{3})(3-\sqrt{3}) = (3)^2 - (\sqrt{3})^2 = 9 - 3 = 6$
$(iii)$ Using the identity $(a+b)^2 = a^2 + b^2 + 2ab$:
$(\sqrt{5}+\sqrt{2})^2 = (\sqrt{5})^2 + (\sqrt{2})^2 + 2(\sqrt{5})(\sqrt{2}) = 5 + 2 + 2\sqrt{10} = 7 + 2\sqrt{10}$
$(iv)$ Using the identity $(a-b)(a+b) = a^2 - b^2$:
$(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2}) = (\sqrt{5})^2 - (\sqrt{2})^2 = 5 - 2 = 3$