Answer
$$(3x-2)(x-2)(x+2)=3x^3-2x^2-12x+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x-2)(x-2)(x+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3x^2-6x-2x+4)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(3x^2-8x+4)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^3+6x^2-8x^2-16x+4x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^3-2x^2-12x+8\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x-2}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{3x-2}\right) \cdot \left( x-2\right) = 3x^2-6x-2x+4 $$ |
| ② | Combine like terms: $$ 3x^2 \color{blue}{-6x} \color{blue}{-2x} +4 = 3x^2 \color{blue}{-8x} +4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{3x^2-8x+4}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{3x^2-8x+4}\right) \cdot \left( x+2\right) = 3x^3+6x^2-8x^2-16x+4x+8 $$ |
| ④ | Combine like terms: $$ 3x^3+ \color{blue}{6x^2} \color{blue}{-8x^2} \color{red}{-16x} + \color{red}{4x} +8 = 3x^3 \color{blue}{-2x^2} \color{red}{-12x} +8 $$ |
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