Question
Answer
$$-10(x+4)(x-5)^2=-10x^3+60x^2+150x-1000$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-10(x+4)(x-5)^2& \xlongequal{ }-10(x+4)(x^2-10x+25) \xlongequal{ } \\[1 em] & \xlongequal{ }-(10x+40)(x^2-10x+25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(10x^3-100x^2+250x+40x^2-400x+1000) \xlongequal{ } \\[1 em] & \xlongequal{ }-(10x^3-60x^2-150x+1000) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-10x^3+60x^2+150x-1000\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{10x+40}\right) $ by each term in $ \left( x^2-10x+25\right) $. $$ \left( \color{blue}{10x+40}\right) \cdot \left( x^2-10x+25\right) = 10x^3-100x^2+250x+40x^2-400x+1000 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(10x^3-60x^2-150x+1000 \right) = -10x^3+60x^2+150x-1000 $$ |
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