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Multiply. Write your answer in simplest form. \newline2v3×(v−3)\frac{2v}{3} \times (v - 3)

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Full solution

Q. Multiply. Write your answer in simplest form. \newline2v3×(v−3)\frac{2v}{3} \times (v - 3)
  1. Rewrite multiplication: Rewrite the multiplication of the fraction and the binomial. So, (2v3)×(v−3)=(2v3)×v1−(2v3)×31(\frac{2v}{3}) \times (v - 3) = (\frac{2v}{3}) \times \frac{v}{1} - (\frac{2v}{3}) \times \frac{3}{1}.
  2. Multiply first term: Multiply the numerators and denominators separately for the first term. So, (2v3)×v1=2v×v3×1=2v23(\frac{2v}{3}) \times \frac{v}{1} = \frac{2v \times v}{3 \times 1} = \frac{2v^2}{3}.
  3. Multiply second term: Multiply the numerators and denominators separately for the second term. So, (2v3)×31=2v×33×1=6v3(\frac{2v}{3}) \times \frac{3}{1} = \frac{2v \times 3}{3 \times 1} = \frac{6v}{3}.
  4. Simplify second term: Simplify the second term. Since 6v3\frac{6v}{3} is divisible by 33, we can simplify it to 2v2v.
  5. Combine terms: Combine the two terms. So, 2v23−2v\frac{2v^2}{3} - 2v.
  6. Final simplification: Since there are no like terms to combine further and no common factors to simplify, the expression is already in its simplest form.

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