Answer
$$-5(x-2)(x-4)(x+1)=-5x^3+25x^2-10x-40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-5(x-2)(x-4)(x+1)& \xlongequal{ }-(5x-10)(x-4)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ }-(5x^2-20x-10x+40)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ }-(5x^2-30x+40)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(5x^3+5x^2-30x^2-30x+40x+40) \xlongequal{ } \\[1 em] & \xlongequal{ }-(5x^3-25x^2+10x+40) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-5x^3+25x^2-10x-40\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5x^2-30x+40}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{5x^2-30x+40}\right) \cdot \left( x+1\right) = 5x^3+5x^2-30x^2-30x+40x+40 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(5x^3-25x^2+10x+40 \right) = -5x^3+25x^2-10x-40 $$ |
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