Question
Answer
$$-100x(x+4)(x-5)=-100x^3+100x^2+2000x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-100x(x+4)(x-5)& \xlongequal{ }-(100x^2+400x)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(100x^3-500x^2+400x^2-2000x) \xlongequal{ } \\[1 em] & \xlongequal{ }-(100x^3-100x^2-2000x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-100x^3+100x^2+2000x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{100x^2+400x}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{100x^2+400x}\right) \cdot \left( x-5\right) = 100x^3-500x^2+400x^2-2000x $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(100x^3-100x^2-2000x \right) = -100x^3+100x^2+2000x $$ |
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