Multiply. Write your answer in simplest form. 4k - 3/5k * (k^2 - 1) ______

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Write Problem: Write down the given problem. We are given the expression (4k - 3)/(5k) * (k^2 - 1).Factor Second Expression: Factor the second expression if possible. The second expression (k^2 - 1) is a difference of squares and can be factored into (k + 1)(k - 1).Rewrite with Factored Form: Rewrite the expression with the factored form. The expression now looks like (4k - 3)/(5k) * (k + 1)(k - 1).Multiply Numerators and Denominators: Multiply the numerators and denominators. When multiplying fractions, we multiply the numerators together and the denominators together. This gives us (4k - 3) * (k + 1)(k - 1) / (5k).Expand Numerator: Expand the numerator. We need to distribute (4k - 3) across (k + 1)(k - 1). First, multiply (k + 1)(k - 1) to get k^2 - 1. Then distribute: 4k(k^2 - 1) - 3(k^2 - 1).Perform Distribution: Perform the distribution. Calculate 4k(k^2 - 1) which is 4k^3 - 4k and -3(k^2 - 1) which is -3k^2 + 3. The expression becomes 4k^3 - 4k - 3k^2 + 3.Combine Like Terms: Combine like terms in the numerator. There are no like terms to combine in 4k^3 - 4k - 3k^2 + 3. So the numerator remains the same.Write Final Expression: Write the final expression. The final expression is (4k^3 - 3k^2 - 4k + 3) / (5k).

Multiply. Write your answer in simplest form. $\newline$ $\frac{4k - 3}{5k} \times (k^2 - 1)$

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Multiply. Write your answer in simplest form. $\newline$ $\frac{4k - 3}{5k} \times (k^2 - 1)$