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Multiply. Write your answer in simplest form. \newlinej24j+1×9j26j+12j1\frac{j^2}{4j + 1} \times \frac{9j^2 - 6j + 1}{2j - 1}

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Q. Multiply. Write your answer in simplest form. \newlinej24j+1×9j26j+12j1\frac{j^2}{4j + 1} \times \frac{9j^2 - 6j + 1}{2j - 1}
  1. Identify expressions to multiply: Identify the expressions to be multiplied.\newlineWe have two fractions to multiply: j24j+1\frac{j^2}{4j + 1} and 9j26j+12j1\frac{9j^2 - 6j + 1}{2j - 1}.
  2. Multiply numerators and denominators: Multiply the numerators and the denominators. The product of the two fractions is (j2×(9j26j+1))/((4j+1)×(2j1))(j^2 \times (9j^2 - 6j + 1)) / ((4j + 1) \times (2j - 1)).
  3. Expand numerators and denominators: Expand the numerators and the denominators.\newlineWe need to multiply j2j^2 with each term in the second numerator and (4j+1)(4j + 1) with each term in the second denominator.\newlineNumerator: j2×9j2j2×6j+j2×1j^2 \times 9j^2 - j^2 \times 6j + j^2 \times 1\newlineDenominator: (4j+1)×(2j1)(4j + 1) \times (2j - 1)
  4. Perform multiplication in numerator: Perform the multiplication in the numerator.\newlineNumerator becomes: 9j46j3+j29j^4 - 6j^3 + j^2
  5. Perform multiplication in denominator: Perform the multiplication in the denominator using the FOIL method (First, Outer, Inner, Last).\newlineDenominator becomes: (4j×2j)+(4j×1)+(1×2j)+(1×1)(4j \times 2j) + (4j \times -1) + (1 \times 2j) + (1 \times -1)
  6. Simplify the denominator: Simplify the denominator.\newlineDenominator becomes: 8j24j+2j18j^2 - 4j + 2j - 1
  7. Combine like terms in denominator: Combine like terms in the denominator.\newlineDenominator becomes: 8j22j18j^2 - 2j - 1
  8. Write simplified product: Write the simplified product of the two fractions.\newlineThe product is (9j46j3+j2)/(8j22j1)(9j^4 - 6j^3 + j^2) / (8j^2 - 2j - 1).
  9. Check for common factors: Check for any common factors that can be canceled out.\newlineThere are no common factors between the numerator and the denominator that can be canceled out.

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