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\left(\sqrt{6}\right)^{2}-7\sqrt{6}+\sqrt{6}-7
Apply the distributive property by multiplying each term of \sqrt{6}+1 by each term of \sqrt{6}-7.
6-7\sqrt{6}+\sqrt{6}-7
The square of \sqrt{6} is 6.
6-6\sqrt{6}-7
Combine -7\sqrt{6} and \sqrt{6} to get -6\sqrt{6}.
-1-6\sqrt{6}
Subtract 7 from 6 to get -1.