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\left(\sqrt{2}\right)^{2}+5\sqrt{2}+3\sqrt{2}+15
Apply the distributive property by multiplying each term of \sqrt{2}+3 by each term of \sqrt{2}+5.
2+5\sqrt{2}+3\sqrt{2}+15
The square of \sqrt{2} is 2.
2+8\sqrt{2}+15
Combine 5\sqrt{2} and 3\sqrt{2} to get 8\sqrt{2}.
17+8\sqrt{2}
Add 2 and 15 to get 17.