Answer
$$(2x+1)(x+3)(3x+7)=6x^3+35x^2+58x+21$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x+1)(x+3)(3x+7)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2+6x+x+3)(3x+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2+7x+3)(3x+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x^3+14x^2+21x^2+49x+9x+21 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6x^3+35x^2+58x+21\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x+1}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{2x+1}\right) \cdot \left( x+3\right) = 2x^2+6x+x+3 $$ |
| ② | Combine like terms: $$ 2x^2+ \color{blue}{6x} + \color{blue}{x} +3 = 2x^2+ \color{blue}{7x} +3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2+7x+3}\right) $ by each term in $ \left( 3x+7\right) $. $$ \left( \color{blue}{2x^2+7x+3}\right) \cdot \left( 3x+7\right) = 6x^3+14x^2+21x^2+49x+9x+21 $$ |
| ④ | Combine like terms: $$ 6x^3+ \color{blue}{14x^2} + \color{blue}{21x^2} + \color{red}{49x} + \color{red}{9x} +21 = 6x^3+ \color{blue}{35x^2} + \color{red}{58x} +21 $$ |
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