Question
Answer
$$2x^2(x-1)-3x(2x+x^2)=-x^3-8x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2x^2(x-1)-3x(2x+x^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2x^3-2x^2-(6x^2+3x^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^3-2x^2-6x^2-3x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^3-8x^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2x^2} $ by $ \left( x-1\right) $ $$ \color{blue}{2x^2} \cdot \left( x-1\right) = 2x^3-2x^2 $$Multiply $ \color{blue}{3x} $ by $ \left( 2x+x^2\right) $ $$ \color{blue}{3x} \cdot \left( 2x+x^2\right) = 6x^2+3x^3 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6x^2+3x^3 \right) = -6x^2-3x^3 $$ |
| ③ | Combine like terms: $$ \color{blue}{2x^3} \color{red}{-2x^2} \color{red}{-6x^2} \color{blue}{-3x^3} = \color{blue}{-x^3} \color{red}{-8x^2} $$ |
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