Answer
$$(9-p)(p^2+8p+12)-3p+9(4p-12)=-p^3+p^2+93p$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(9-p)(p^2+8p+12)-3p+9(4p-12)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9p^2+72p+108-p^3-8p^2-12p-3p+36p-108 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-p^3+p^2+57p+108+36p-108 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-p^3+p^2+93p\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{9-p}\right) $ by each term in $ \left( p^2+8p+12\right) $. $$ \left( \color{blue}{9-p}\right) \cdot \left( p^2+8p+12\right) = 9p^2+72p+108-p^3-8p^2-12p $$Multiply $ \color{blue}{9} $ by $ \left( 4p-12\right) $ $$ \color{blue}{9} \cdot \left( 4p-12\right) = 36p-108 $$ |
| ② | Combine like terms: $$ \color{blue}{9p^2} + \color{red}{72p} +108-p^3 \color{blue}{-8p^2} \color{green}{-12p} \color{green}{-3p} = -p^3+ \color{blue}{p^2} + \color{green}{57p} +108 $$ |
| ③ | Combine like terms: $$ -p^3+p^2+ \color{blue}{57p} + \, \color{red}{ \cancel{108}} \,+ \color{blue}{36p} \, \color{red}{ -\cancel{108}} \, = -p^3+p^2+ \color{blue}{93p} $$ |
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