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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}: We need to 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 −5-5: Now we multiply 2\sqrt{2} by −5-5.2×(−5)=−52\sqrt{2} \times (-5) = -5 \sqrt{2}
  3. Multiply by −5-\sqrt{5}: Next, we multiply 2\sqrt{2} by −5-\sqrt{5}.\newline2×(−5)=−2×5\sqrt{2} \times (-\sqrt{5}) = -\sqrt{2} \times \sqrt{5}
  4. Apply product rule: Apply the product rule of radicals for −2×5-\sqrt{2} \times \sqrt{5}.−2×5=−2×5=−10-\sqrt{2} \times \sqrt{5} = -\sqrt{2 \times 5} = -\sqrt{10}
  5. Combine products: Combine the two products to write the expression in simplest form. \newline−52−10-5 \sqrt{2} - \sqrt{10}

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