Answer
$$-3(x-1)(x+3)(x-2)=-3x^3+21x-18$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3(x-1)(x+3)(x-2)& \xlongequal{ }-(3x-3)(x+3)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ }-(3x^2+9x-3x-9)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ }-(3x^2+6x-9)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(3x^3-6x^2+6x^2-12x-9x+18) \xlongequal{ } \\[1 em] & \xlongequal{ }-(3x^3-21x+18) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-3x^3+21x-18\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x^2+6x-9}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{3x^2+6x-9}\right) \cdot \left( x-2\right) = 3x^3 -\cancel{6x^2}+ \cancel{6x^2}-12x-9x+18 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(3x^3-21x+18 \right) = -3x^3+21x-18 $$ |
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