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Multiply. Write your answer in simplest form. \newline5(−6+2)\sqrt{5}(-6 + \sqrt{2})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline5(−6+2)\sqrt{5}(-6 + \sqrt{2})
  1. Distribute 5\sqrt{5}: Distribute 5\sqrt{5} to both terms inside the parentheses.\newline5(−6+2)\sqrt{5}(-6 + \sqrt{2})\newline= 5⋅(−6)+5⋅(2)\sqrt{5}\cdot(-6) + \sqrt{5}\cdot(\sqrt{2})
  2. Multiply by −6-6: Multiply 5\sqrt{5} by −6-6.5×(−6)=−6×5\sqrt{5} \times (-6) = -6 \times \sqrt{5}
  3. Multiply by 2\sqrt{2}: Multiply 5\sqrt{5} by 2\sqrt{2}.5×2\sqrt{5} \times \sqrt{2}=5×2= \sqrt{5 \times 2}=10= \sqrt{10}
  4. Combine results: Combine the results from Step 22 and Step 33.\newline−6×5+10-6 \times \sqrt{5} + \sqrt{10}

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