Answer
$$(x-2)(3x+2)(2x+3)=6x^3+x^2-20x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(3x+2)(2x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3x^2+2x-6x-4)(2x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(3x^2-4x-4)(2x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x^3+9x^2-8x^2-12x-8x-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6x^3+x^2-20x-12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( 3x+2\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( 3x+2\right) = 3x^2+2x-6x-4 $$ |
| ② | Combine like terms: $$ 3x^2+ \color{blue}{2x} \color{blue}{-6x} -4 = 3x^2 \color{blue}{-4x} -4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{3x^2-4x-4}\right) $ by each term in $ \left( 2x+3\right) $. $$ \left( \color{blue}{3x^2-4x-4}\right) \cdot \left( 2x+3\right) = 6x^3+9x^2-8x^2-12x-8x-12 $$ |
| ④ | Combine like terms: $$ 6x^3+ \color{blue}{9x^2} \color{blue}{-8x^2} \color{red}{-12x} \color{red}{-8x} -12 = 6x^3+ \color{blue}{x^2} \color{red}{-20x} -12 $$ |
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