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Multiply. Write your answer in simplest form. $\newline$ $\frac{6m}{5} \times (4m - 5)$

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Multiply and divide rational expressions

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Q. Multiply. Write your answer in simplest form.

\newline

\frac{6m}{5} \times (4m - 5)

Identify Expression: Identify the expression to be simplified. $\newline$ We are given the expression $\frac{6m}{5} \times (4m - 5)$ . We need to multiply the fraction by the binomial.
Distribute Fraction: Distribute the fraction across the binomial. $\newline$ To multiply the fraction by the binomial, we distribute the fraction to each term in the binomial: $\newline$ $(\frac{6m}{5}) \times 4m + (\frac{6m}{5}) \times (-5)$
Perform Multiplication: Perform the multiplication for each term. $\newline$ Now we multiply the fraction by each term in the binomial separately: $\newline$ $(\frac{6m}{5}) \times 4m = \frac{(6m \times 4m)}{5}$ $\newline$ $(\frac{6m}{5}) \times (-5) = \frac{(6m \times -5)}{5}$
Simplify Terms: Simplify each term. $\newline$ We simplify the multiplication for each term: $\newline$ $(6m \times 4m) / 5 = (24m^2) / 5$ $\newline$ $(6m \times -5) / 5 = (-30m) / 5$
Reduce Terms: Reduce each term, if possible. $\newline$ We check if each term can be reduced further: $\newline$ $(24m^2) / 5$ cannot be reduced as $5$ is not a factor of $24$ . $\newline$ $(-30m) / 5$ can be reduced because $5$ is a factor of $-30$ : $\newline$ $(-30m) / 5 = -6m$
Combine Final Expression: Combine the simplified terms. $\newline$ Now we combine the two terms to get the final expression: $\newline$ $(\frac{24m^2}{5}) - 6m$

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