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8\left(\sqrt{3}\right)^{2}+8\sqrt{3}-7\sqrt{3}-7
Apply the distributive property by multiplying each term of 8\sqrt{3}-7 by each term of \sqrt{3}+1.
8\times 3+8\sqrt{3}-7\sqrt{3}-7
The square of \sqrt{3} is 3.
24+8\sqrt{3}-7\sqrt{3}-7
Multiply 8 and 3 to get 24.
24+\sqrt{3}-7
Combine 8\sqrt{3} and -7\sqrt{3} to get \sqrt{3}.
17+\sqrt{3}
Subtract 7 from 24 to get 17.