Answer
$$3(2x+8)(x+2)\cdot3(x-3)\cdot3=54x^3+162x^2-540x-1296$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(2x+8)(x+2)\cdot3(x-3)\cdot3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6x+24)(x+2)\cdot3(x-3)\cdot3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6x^2+12x+24x+48)\cdot3(x-3)\cdot3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(6x^2+36x+48)\cdot3(x-3)\cdot3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(18x^2+108x+144)(x-3)\cdot3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(18x^3-54x^2+108x^2-324x+144x-432)\cdot3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}(18x^3+54x^2-180x-432)\cdot3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}54x^3+162x^2-540x-1296\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 2x+8\right) $ $$ \color{blue}{3} \cdot \left( 2x+8\right) = 6x+24 $$ |
| ② | Multiply each term of $ \left( \color{blue}{6x+24}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{6x+24}\right) \cdot \left( x+2\right) = 6x^2+12x+24x+48 $$ |
| ③ | Combine like terms: $$ 6x^2+ \color{blue}{12x} + \color{blue}{24x} +48 = 6x^2+ \color{blue}{36x} +48 $$ |
| ④ | $$ \left( \color{blue}{6x^2+36x+48}\right) \cdot 3 = 18x^2+108x+144 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{18x^2+108x+144}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{18x^2+108x+144}\right) \cdot \left( x-3\right) = 18x^3-54x^2+108x^2-324x+144x-432 $$ |
| ⑥ | Combine like terms: $$ 18x^3 \color{blue}{-54x^2} + \color{blue}{108x^2} \color{red}{-324x} + \color{red}{144x} -432 = 18x^3+ \color{blue}{54x^2} \color{red}{-180x} -432 $$ |
| ⑦ | $$ \left( \color{blue}{18x^3+54x^2-180x-432}\right) \cdot 3 = 54x^3+162x^2-540x-1296 $$ |
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