Answer
$$3m(6m^2-5m+4)-(4m^3-8m^2+9)=14m^3-7m^2+12m-9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3m(6m^2-5m+4)-(4m^3-8m^2+9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}18m^3-15m^2+12m-(4m^3-8m^2+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}18m^3-15m^2+12m-4m^3+8m^2-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}14m^3-7m^2+12m-9\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3m} $ by $ \left( 6m^2-5m+4\right) $ $$ \color{blue}{3m} \cdot \left( 6m^2-5m+4\right) = 18m^3-15m^2+12m $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4m^3-8m^2+9 \right) = -4m^3+8m^2-9 $$ |
| ③ | Combine like terms: $$ \color{blue}{18m^3} \color{red}{-15m^2} +12m \color{blue}{-4m^3} + \color{red}{8m^2} -9 = \color{blue}{14m^3} \color{red}{-7m^2} +12m-9 $$ |
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