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$\displaystyle 1)..( \sqrt{8}-3)(3+2 \sqrt{2})=( \sqrt{2^{2}*2}-3)(2 \sqrt{2}+3)= \\ =(2 \sqrt{2}-3)(2 \sqrt{2}+3)=(2 \sqrt{2})^{2}-3^{2}=4*2-9=8-9=-1 \\ \\ 2)..( \sqrt{27}-2)(2-3 \sqrt{3})-12 \sqrt{3}=( \sqrt{3^{3}}-2)(2-3 \sqrt{3})-12 \sqrt{3}= \\ =-(3 \sqrt{3}-2)(3 \sqrt{3}-2)-12 \sqrt{3}=-(3 \sqrt{3}-2)^{2}-12 \sqrt{3}= \\ =-(27-12 \sqrt{3}+4)-12 \sqrt{3}=-27-4=-31\\\\3).. (\sqrt{50}+4 \sqrt{2})* \sqrt{2}= \sqrt{50*2}+4 \sqrt{2*2}=10+8=18$
$\displaystyle 4)..(5\sqrt{3}+\sqrt{27}):\sqrt{3}=\frac{5\sqrt{3}}{\sqrt{3}}+\frac{3 \sqrt{3}}{\sqrt{3}}=5+3=8\\\\5)..(2\sqrt{3}-1)^{2}+(2 \sqrt{3}+1)^{2}=4*3-4 \sqrt{3}+1+4*3+4\sqrt{3}+1=26\\\\6)..(\sqrt{5}-1)^{2}+(2\sqrt{5}+1)^{2}-2 \sqrt{5}= \\ =5-2\sqrt{5}+1+4*5+4\sqrt{5}+1-2\sqrt{5}=27$