Answer
$$2(-n+5n^2+9)-3\cdot(3-n)=10n^2+n+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(-n+5n^2+9)-3\cdot(3-n)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-2n+10n^2+18-(9-3n) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2n+10n^2+18-9+3n \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10n^2+n+9\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( -n+5n^2+9\right) $ $$ \color{blue}{2} \cdot \left( -n+5n^2+9\right) = -2n+10n^2+18 $$Multiply $ \color{blue}{3} $ by $ \left( 3-n\right) $ $$ \color{blue}{3} \cdot \left( 3-n\right) = 9-3n $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9-3n \right) = -9+3n $$ |
| ③ | Combine like terms: $$ \color{blue}{-2n} +10n^2+ \color{red}{18} \color{red}{-9} + \color{blue}{3n} = 10n^2+ \color{blue}{n} + \color{red}{9} $$ |
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