Answer
$$-2(x+1)(x-3)^2=-2x^3+10x^2-6x-18$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-2(x+1)(x-3)^2& \xlongequal{ }-2(x+1)(x^2-6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x+2)(x^2-6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(2x^3-12x^2+18x+2x^2-12x+18) \xlongequal{ } \\[1 em] & \xlongequal{ }-(2x^3-10x^2+6x+18) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2x^3+10x^2-6x-18\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x+2}\right) $ by each term in $ \left( x^2-6x+9\right) $. $$ \left( \color{blue}{2x+2}\right) \cdot \left( x^2-6x+9\right) = 2x^3-12x^2+18x+2x^2-12x+18 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(2x^3-10x^2+6x+18 \right) = -2x^3+10x^2-6x-18 $$ |
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