Answer
$$(3x+5)(x-2)(x+4)=3x^3+11x^2-14x-40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x+5)(x-2)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3x^2-6x+5x-10)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(3x^2-x-10)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^3+12x^2-x^2-4x-10x-40 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^3+11x^2-14x-40\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x+5}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{3x+5}\right) \cdot \left( x-2\right) = 3x^2-6x+5x-10 $$ |
| ② | Combine like terms: $$ 3x^2 \color{blue}{-6x} + \color{blue}{5x} -10 = 3x^2 \color{blue}{-x} -10 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{3x^2-x-10}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{3x^2-x-10}\right) \cdot \left( x+4\right) = 3x^3+12x^2-x^2-4x-10x-40 $$ |
| ④ | Combine like terms: $$ 3x^3+ \color{blue}{12x^2} \color{blue}{-x^2} \color{red}{-4x} \color{red}{-10x} -40 = 3x^3+ \color{blue}{11x^2} \color{red}{-14x} -40 $$ |
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