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

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Full solution

Q. Multiply. Write your answer in simplest form. \newline2(5−3)\sqrt{2}(5 - \sqrt{3})
  1. Distribute 2\sqrt{2}: Distribute 2\sqrt{2} across the terms inside the parentheses.2(5−3)=2×5+2×(−3)\sqrt{2}(5 - \sqrt{3}) = \sqrt{2} \times 5 + \sqrt{2} \times (-\sqrt{3})
  2. Multiply by 55: Multiply 2\sqrt{2} by 55.2×5=52\sqrt{2} \times 5 = 5\sqrt{2}
  3. Multiply by −3-\sqrt{3}: Multiply 2\sqrt{2} by −3-\sqrt{3}.\newline2×(−3)=−2×3\sqrt{2} \times (-\sqrt{3}) = -\sqrt{2 \times 3}
  4. Simplify radical expression: Simplify the radical expression. −2×3=−6-\sqrt{2 \times 3} = -\sqrt{6}
  5. Combine results: Combine the two results to get the final answer. 52−65\sqrt{2} - \sqrt{6}

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