Subtract \[(-20-12sqrt(17))\] from \[(-14+4sqrt(17))\] Choose 1 answer: A \[6+16sqrt(17)\] B \[-6+16sqrt(17)\] C \[-6-16sqrt(17)\] D \[6-16sqrt(17)\] Related content

Mathematics

ScanSolve AI Answer

Answer

6+16176+16\sqrt{17}

Step-by-step solution

3 steps

To subtract the first expression from the second, we write it as:

(−14+417)−(−20−1217)(-14+4\sqrt{17}) - (-20-12\sqrt{17})
  1. Distribute the negative sign

    When subtracting a parenthesized expression, we change the sign of each term inside the parentheses.

    −14+417+20+1217-14+4\sqrt{17} + 20 + 12\sqrt{17}
  2. Group like terms

    Group the constant terms and the terms containing 17\sqrt{17}.

    (−14+20)+(417+1217)(-14 + 20) + (4\sqrt{17} + 12\sqrt{17})
  3. Combine like terms

    Perform the addition for the constant terms and for the terms with 17\sqrt{17}.

    (6)+(4+12)17(6) + (4+12)\sqrt{17} 6+16176 + 16\sqrt{17}
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