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Multiply. Write your answer in simplest form. \newline−2(5−5)-\sqrt{2}(5 - \sqrt{5})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline−2(5−5)-\sqrt{2}(5 - \sqrt{5})
  1. Distribute −2-\sqrt{2}: First, distribute −2-\sqrt{2} across the parentheses.−2×(5−5)=−2×5+2×5-\sqrt{2} \times (5 - \sqrt{5}) = -\sqrt{2} \times 5 + \sqrt{2} \times \sqrt{5}
  2. Multiply −2-\sqrt{2} by 55: Now, multiply −2-\sqrt{2} by 55.\newline−2×5=−52-\sqrt{2} \times 5 = -5\sqrt{2}
  3. Multiply 2\sqrt{2} by 5\sqrt{5}: Next, multiply 2\sqrt{2} by 5\sqrt{5}.\newline2×5=2×5=10\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} = \sqrt{10}
  4. Combine the results: Finally, combine the two results. −52+10-5\sqrt{2} + \sqrt{10}

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