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

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Full solution

Q. Multiply. Write your answer in simplest form. \newline−5(−2+5)-\sqrt{5}(-2 + \sqrt{5})
  1. Distribute −5-\sqrt{5}: Distribute −5-\sqrt{5} to both terms inside the parentheses.−5(−2+5)=−5(−2)+−55-\sqrt{5}(-2 + \sqrt{5}) = -\sqrt{5}(-2) + -\sqrt{5}\sqrt{5}
  2. Multiply −5-\sqrt{5} by −2-2: Multiply −5-\sqrt{5} by −2-2.−5⋅(−2)=25-\sqrt{5}\cdot(-2) = 2\sqrt{5}
  3. Multiply −5-\sqrt{5} by 5\sqrt{5}: Multiply −5-\sqrt{5} by 5\sqrt{5}.−5×5-\sqrt{5}\times\sqrt{5} = −(5)2-(\sqrt{5})^2 = −5-5 because the square root and the square cancel each other out.
  4. Combine the results: Combine the results from Step 22 and Step 33.\newline25−52\sqrt{5} - 5\newlineThis is the simplest form of the expression.

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