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1) $7\sqrt{6}-2\sqrt{54}+\sqrt{96}=7\sqrt{6}-2\sqrt{9}\sqrt{6}+\sqrt{16}\sqrt{6}=7\sqrt{6}-6\sqrt{6}+4\sqrt{6}=5\sqrt{6}$

$(\sqrt{80}-\sqrt{20})\sqrt{5}=\sqrt{80*5}-\sqrt{20*5}=\sqrt{400}-\sqrt{100}=20-10=10$

$(\sqrt{10}-1)^2=(\sqrt{10})^2-2*\sqrt{10}*1+1^2=10+1-2\sqrt{10}=11-2\sqrt{10}$

$(6\sqrt{3}+\sqrt{2})(6\sqrt{3}-\sqrt{2})=(6\sqrt{3})^2-(\sqrt{2})^2=36*3-2=108-2=106$