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Multiply. Write your answer in simplest form. \newline5(−7−2)\sqrt{5}(-7 - \sqrt{2})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline5(−7−2)\sqrt{5}(-7 - \sqrt{2})
  1. Distribute 5\sqrt{5}: We need to distribute 5\sqrt{5} across the terms inside the parentheses.5(−7−2)=5×−7+5×−2\sqrt{5}(-7 - \sqrt{2}) = \sqrt{5} \times -7 + \sqrt{5} \times -\sqrt{2}
  2. Multiply by −7-7: Now we multiply 5\sqrt{5} by −7-7.5×−7=−75\sqrt{5} \times -7 = -7\sqrt{5}
  3. Multiply by −2-\sqrt{2}: Next, we multiply 5\sqrt{5} by −2-\sqrt{2}.\newline5×−2=−5×2=−10\sqrt{5} \times -\sqrt{2} = -\sqrt{5 \times 2} = -\sqrt{10}
  4. Combine to get final answer: Combine the two products to get the final answer. \newline−75−10-7\sqrt{5} - \sqrt{10}

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