Q. Multiply. Write your answer in simplest form. 4j+1j2×2j−19j2−6j+1
Identify expressions to multiply: Identify the expressions to be multiplied.We have two fractions to multiply: 4j+1j2 and 2j−19j2−6j+1.
Multiply numerators and denominators: Multiply the numerators and the denominators. The product of the two fractions is (j2×(9j2−6j+1))/((4j+1)×(2j−1)).
Expand numerators and denominators: Expand the numerators and the denominators.We need to multiply j2 with each term in the second numerator and (4j+1) with each term in the second denominator.Numerator: j2×9j2−j2×6j+j2×1Denominator: (4j+1)×(2j−1)
Perform multiplication in numerator: Perform the multiplication in the numerator.Numerator becomes: 9j4−6j3+j2
Perform multiplication in denominator: Perform the multiplication in the denominator using the FOIL method (First, Outer, Inner, Last).Denominator becomes: (4j×2j)+(4j×−1)+(1×2j)+(1×−1)
Simplify the denominator: Simplify the denominator.Denominator becomes: 8j2−4j+2j−1
Combine like terms in denominator: Combine like terms in the denominator.Denominator becomes: 8j2−2j−1
Write simplified product: Write the simplified product of the two fractions.The product is (9j4−6j3+j2)/(8j2−2j−1).
Check for common factors: Check for any common factors that can be canceled out.There are no common factors between the numerator and the denominator that can be canceled out.
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