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Multiply. Write your answer in simplest form. \newline2(3−5)\sqrt{2}(3 - \sqrt{5})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline2(3−5)\sqrt{2}(3 - \sqrt{5})
  1. Distribute 2\sqrt{2}: We need to distribute 2\sqrt{2} across the terms inside the parentheses.2(3−5)=2×3+2×(−5)\sqrt{2}(3 - \sqrt{5}) = \sqrt{2} \times 3 + \sqrt{2} \times (-\sqrt{5})
  2. Multiply by 33: Now we multiply 2\sqrt{2} by 33.2×3=32\sqrt{2} \times 3 = 3\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 5}
  4. Simplify radical expression: Simplify the radical expression. −2×5=−10-\sqrt{2 \times 5} = -\sqrt{10}
  5. Combine results: Combine the two results to get the final answer. 32−103\sqrt{2} - \sqrt{10}

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