Answer
$$(m^2+3m+2)(2m^2+m+5)=2m^4+7m^3+12m^2+17m+10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(m^2+3m+2)(2m^2+m+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2m^4+7m^3+12m^2+17m+10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{m^2+3m+2}\right) $ by each term in $ \left( 2m^2+m+5\right) $. $$ \left( \color{blue}{m^2+3m+2}\right) \cdot \left( 2m^2+m+5\right) = 2m^4+m^3+5m^2+6m^3+3m^2+15m+4m^2+2m+10 $$ |
| ② | Combine like terms: $$ 2m^4+ \color{blue}{m^3} + \color{red}{5m^2} + \color{blue}{6m^3} + \color{green}{3m^2} + \color{orange}{15m} + \color{green}{4m^2} + \color{orange}{2m} +10 = \\ = 2m^4+ \color{blue}{7m^3} + \color{green}{12m^2} + \color{orange}{17m} +10 $$ |
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