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Multiply. Write your answer in simplest form. \newline2(5−5)\sqrt{2}(5 - \sqrt{5})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline2(5−5)\sqrt{2}(5 - \sqrt{5})
  1. Distribute 2\sqrt{2}: Distribute 2\sqrt{2} across the terms inside the parentheses.2(5−5)=2×5+2×(−5)\sqrt{2}(5 - \sqrt{5}) = \sqrt{2} \times 5 + \sqrt{2} \times (-\sqrt{5})
  2. Multiply by 55: Multiply 2\sqrt{2} by 55.2×5=52\sqrt{2} \times 5 = 5\sqrt{2}
  3. Multiply by −5-\sqrt{5}: Multiply 2\sqrt{2} by −5-\sqrt{5}.2×(−5)=−2×5=−10\sqrt{2} \times (-\sqrt{5}) = -\sqrt{2 \times 5} = -\sqrt{10}
  4. Combine to get final answer: Combine the two results to get the final answer. 52−105\sqrt{2} - \sqrt{10}

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