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Multiply. Write your answer in simplest form. \newline3(−7−2)\sqrt{3}(-7 - \sqrt{2})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline3(−7−2)\sqrt{3}(-7 - \sqrt{2})
  1. Distribute 3\sqrt{3}: Distribute 3\sqrt{3} to both terms inside the parentheses.\newline3(−7−2)\sqrt{3}(-7 - \sqrt{2})\newline= 3×(−7)+3×(−2)\sqrt{3} \times (-7) + \sqrt{3} \times (-\sqrt{2})
  2. Multiply by −7-7: Multiply the square root of 33 by −7-7.3×(−7)=−73\sqrt{3} \times (-7) = -7\sqrt{3}
  3. Multiply by −2-\sqrt{2}: Multiply the square root of 33 by the negative square root of 22.3×(−2)=−3×2=−6\sqrt{3} \times (-\sqrt{2}) = -\sqrt{3 \times 2} = -\sqrt{6}
  4. Combine results: Combine the results from Step 22 and Step 33.\newline−73−6-7\sqrt{3} - \sqrt{6}

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