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

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Full solution

Q. Multiply. Write your answer in simplest form. \newline5(2−2)\sqrt{5}(2 - \sqrt{2})
  1. Distribute 5\sqrt{5}: Distribute 5\sqrt{5} to both terms inside the parentheses.5(2−2)=5⋅2−5⋅2\sqrt{5}(2 - \sqrt{2}) = \sqrt{5}\cdot 2 - \sqrt{5}\cdot\sqrt{2}
  2. Multiply 5\sqrt{5} by 22: Now, multiply 5\sqrt{5} by 22.5×2=25\sqrt{5} \times 2 = 2\sqrt{5}
  3. Multiply 5\sqrt{5} by −2-\sqrt{2}: Next, multiply 5\sqrt{5} by −2-\sqrt{2}.5×(−2)=−5×2=−10\sqrt{5} \times (-\sqrt{2}) = -\sqrt{5 \times 2} = -\sqrt{10}
  4. Combine results: Combine the two results to get the final answer. 25−102\sqrt{5} - \sqrt{10}

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