Answer
$$(n+2)(n+3)(2n+4)=2n^3+14n^2+32n+24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(n+2)(n+3)(2n+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1n^2+3n+2n+6)(2n+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1n^2+5n+6)(2n+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2n^3+4n^2+10n^2+20n+12n+24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2n^3+14n^2+32n+24\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{n+2}\right) $ by each term in $ \left( n+3\right) $. $$ \left( \color{blue}{n+2}\right) \cdot \left( n+3\right) = n^2+3n+2n+6 $$ |
| ② | Combine like terms: $$ n^2+ \color{blue}{3n} + \color{blue}{2n} +6 = n^2+ \color{blue}{5n} +6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{n^2+5n+6}\right) $ by each term in $ \left( 2n+4\right) $. $$ \left( \color{blue}{n^2+5n+6}\right) \cdot \left( 2n+4\right) = 2n^3+4n^2+10n^2+20n+12n+24 $$ |
| ④ | Combine like terms: $$ 2n^3+ \color{blue}{4n^2} + \color{blue}{10n^2} + \color{red}{20n} + \color{red}{12n} +24 = 2n^3+ \color{blue}{14n^2} + \color{red}{32n} +24 $$ |
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