Answer
$$-2x(x^3-6x^2+6)+4x^3-(5x^4+10x)=-7x^4+16x^3-22x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-2x(x^3-6x^2+6)+4x^3-(5x^4+10x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(2x^4-12x^3+12x)+4x^3-(5x^4+10x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2x^4+12x^3-12x+4x^3-(5x^4+10x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^4+16x^3-12x-(5x^4+10x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-2x^4+16x^3-12x-5x^4-10x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-7x^4+16x^3-22x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2x} $ by $ \left( x^3-6x^2+6\right) $ $$ \color{blue}{2x} \cdot \left( x^3-6x^2+6\right) = 2x^4-12x^3+12x $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(2x^4-12x^3+12x \right) = -2x^4+12x^3-12x $$ |
| ③ | Combine like terms: $$ -2x^4+ \color{blue}{12x^3} -12x+ \color{blue}{4x^3} = -2x^4+ \color{blue}{16x^3} -12x $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5x^4+10x \right) = -5x^4-10x $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-2x^4} +16x^3 \color{red}{-12x} \color{blue}{-5x^4} \color{red}{-10x} = \color{blue}{-7x^4} +16x^3 \color{red}{-22x} $$ |
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