Question
Answer
$$-(x+1)^3(x-2)=-x^4-x^3+3x^2+5x+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-(x+1)^3(x-2)& \xlongequal{ }-(x^3+3x^2+3x+1)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(x^4+x^3-3x^2-5x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^4-x^3+3x^2+5x+2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^3+3x^2+3x+1}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x^3+3x^2+3x+1}\right) \cdot \left( x-2\right) = x^4-2x^3+3x^3-6x^2+3x^2-6x+x-2 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-2x^3} + \color{blue}{3x^3} \color{red}{-6x^2} + \color{red}{3x^2} \color{green}{-6x} + \color{green}{x} -2 = x^4+ \color{blue}{x^3} \color{red}{-3x^2} \color{green}{-5x} -2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(x^4+x^3-3x^2-5x-2 \right) = -x^4-x^3+3x^2+5x+2 $$ |
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