Multiply. Write your answer in simplest form. 6m/5 * (4m - 5) ______

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

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Math Problems

Algebra 2

Multiply and divide rational expressions

Full solution

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: $\newline$ $(\frac{24m^2}{5}) - 6m$