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10\sqrt{7}-4\sqrt{7}\sqrt{2}+15\sqrt{2}-6\left(\sqrt{2}\right)^{2}
Apply the distributive property by multiplying each term of 2\sqrt{7}+3\sqrt{2} by each term of 5-2\sqrt{2}.
10\sqrt{7}-4\sqrt{14}+15\sqrt{2}-6\left(\sqrt{2}\right)^{2}
To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.
10\sqrt{7}-4\sqrt{14}+15\sqrt{2}-6\times 2
The square of \sqrt{2} is 2.
10\sqrt{7}-4\sqrt{14}+15\sqrt{2}-12
Multiply -6 and 2 to get -12.