Answer
$$(n+1)(n+2)(2n+3)=2n^3+9n^2+13n+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(n+1)(n+2)(2n+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1n^2+2n+n+2)(2n+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1n^2+3n+2)(2n+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2n^3+3n^2+6n^2+9n+4n+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2n^3+9n^2+13n+6\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{n+1}\right) $ by each term in $ \left( n+2\right) $. $$ \left( \color{blue}{n+1}\right) \cdot \left( n+2\right) = n^2+2n+n+2 $$ |
| ② | Combine like terms: $$ n^2+ \color{blue}{2n} + \color{blue}{n} +2 = n^2+ \color{blue}{3n} +2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{n^2+3n+2}\right) $ by each term in $ \left( 2n+3\right) $. $$ \left( \color{blue}{n^2+3n+2}\right) \cdot \left( 2n+3\right) = 2n^3+3n^2+6n^2+9n+4n+6 $$ |
| ④ | Combine like terms: $$ 2n^3+ \color{blue}{3n^2} + \color{blue}{6n^2} + \color{red}{9n} + \color{red}{4n} +6 = 2n^3+ \color{blue}{9n^2} + \color{red}{13n} +6 $$ |
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