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Multiply. Write your answer in simplest form. \newline2(−7+5)\sqrt{2}(-7 + \sqrt{5})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline2(−7+5)\sqrt{2}(-7 + \sqrt{5})
  1. Distribute 2\sqrt{2}: Distribute 2\sqrt{2} across the terms inside the parentheses.\newline2(−7+5)=2×−7+2×5\sqrt{2}(-7 + \sqrt{5}) = \sqrt{2} \times -7 + \sqrt{2} \times \sqrt{5}
  2. Multiply by −7-7: Multiply 2\sqrt{2} by −7-7.\newline2×−7=−72\sqrt{2} \times -7 = -7\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. \newline−72+10-7\sqrt{2} + \sqrt{10}

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