Answer
$$5n(n+1)(3n^2+7n+5)=15n^4+50n^3+60n^2+25n$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5n(n+1)(3n^2+7n+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(5n^2+5n)(3n^2+7n+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}15n^4+35n^3+25n^2+15n^3+35n^2+25n \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}15n^4+50n^3+60n^2+25n\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{5n} $ by $ \left( n+1\right) $ $$ \color{blue}{5n} \cdot \left( n+1\right) = 5n^2+5n $$ |
| ② | Multiply each term of $ \left( \color{blue}{5n^2+5n}\right) $ by each term in $ \left( 3n^2+7n+5\right) $. $$ \left( \color{blue}{5n^2+5n}\right) \cdot \left( 3n^2+7n+5\right) = 15n^4+35n^3+25n^2+15n^3+35n^2+25n $$ |
| ③ | Combine like terms: $$ 15n^4+ \color{blue}{35n^3} + \color{red}{25n^2} + \color{blue}{15n^3} + \color{red}{35n^2} +25n = 15n^4+ \color{blue}{50n^3} + \color{red}{60n^2} +25n $$ |
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