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