Question
Answer
$$-(x-1)^2(x+4)=-x^3-2x^2+7x-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-(x-1)^2(x+4)& \xlongequal{ }-(x^2-2x+1)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(x^3+4x^2-2x^2-8x+x+4) \xlongequal{ } \\[1 em] & \xlongequal{ }-(x^3+2x^2-7x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-x^3-2x^2+7x-4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-2x+1}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x^2-2x+1}\right) \cdot \left( x+4\right) = x^3+4x^2-2x^2-8x+x+4 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(x^3+2x^2-7x+4 \right) = -x^3-2x^2+7x-4 $$ |
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