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2\left(\sqrt{2}\right)^{2}+\sqrt{2}-6\sqrt{2}-3
Apply the distributive property by multiplying each term of \sqrt{2}-3 by each term of 2\sqrt{2}+1.
2\times 2+\sqrt{2}-6\sqrt{2}-3
The square of \sqrt{2} is 2.
4+\sqrt{2}-6\sqrt{2}-3
Multiply 2 and 2 to get 4.
4-5\sqrt{2}-3
Combine \sqrt{2} and -6\sqrt{2} to get -5\sqrt{2}.
1-5\sqrt{2}
Subtract 3 from 4 to get 1.