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Multiply. Write your answer in simplest form. \newline2(8+2)\sqrt{2}(8 + \sqrt{2})

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Full solution

Q. Multiply. Write your answer in simplest form. \newline2(8+2)\sqrt{2}(8 + \sqrt{2})
  1. Distribute 2\sqrt{2}: We need to distribute 2\sqrt{2} across the terms inside the parentheses.2(8+2)=2×8+2×2\sqrt{2}(8 + \sqrt{2}) = \sqrt{2} \times 8 + \sqrt{2} \times \sqrt{2}
  2. Multiply by 88: Now we multiply 2\sqrt{2} by 88.2×8=82\sqrt{2} \times 8 = 8\sqrt{2}
  3. Multiply by 2\sqrt{2}: Next, we multiply 2\sqrt{2} by 2\sqrt{2}.2×2=2\sqrt{2} \times \sqrt{2} = 2This is because the square root of a number times itself equals the number.
  4. Combine results: Now we combine the two results to get the final answer. 82+28\sqrt{2} + 2 This is already in simplest form.

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