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20+4\sqrt{2}-5\sqrt{2}-\left(\sqrt{2}\right)^{2}
Apply the distributive property by multiplying each term of 4-\sqrt{2} by each term of 5+\sqrt{2}.
20-\sqrt{2}-\left(\sqrt{2}\right)^{2}
Combine 4\sqrt{2} and -5\sqrt{2} to get -\sqrt{2}.
20-\sqrt{2}-2
The square of \sqrt{2} is 2.
18-\sqrt{2}
Subtract 2 from 20 to get 18.