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

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Full solution

Q. Multiply. Write your answer in simplest form. \newline2(−2+5)\sqrt{2}(-2 + \sqrt{5})
  1. Distribute 2\sqrt{2}: Distribute 2\sqrt{2} to both terms inside the parentheses.2(−2+5)\sqrt{2}(-2 + \sqrt{5}) = 2×(−2)\sqrt{2} \times (-2) + 2×5\sqrt{2} \times \sqrt{5}
  2. Multiply 2\sqrt{2} by −2-2: Multiply 2\sqrt{2} by −2-2.\newline2×(−2)=−2×2\sqrt{2} \times (-2) = -2 \times \sqrt{2}
  3. Multiply 2\sqrt{2} by 5\sqrt{5}: Multiply 2\sqrt{2} by 5\sqrt{5}.\newline2×5=2×5=10\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} = \sqrt{10}
  4. Combine results: Combine the results from Step 22 and Step 33.\newline−2×2+10-2 \times \sqrt{2} + \sqrt{10}

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