Answer
$$-x(6+2x)^2(3-x)^2=-4x^5+72x^3-324x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-x(6+2x)^2(3-x)^2& \xlongequal{ }-x(36+24x+4x^2)(9-6x+x^2) \xlongequal{ } \\[1 em] & \xlongequal{ }-(36x+24x^2+4x^3)(9-6x+x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(4x^5-72x^3+324x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-4x^5+72x^3-324x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{36x+24x^2+4x^3}\right) $ by each term in $ \left( 9-6x+x^2\right) $. $$ \left( \color{blue}{36x+24x^2+4x^3}\right) \cdot \left( 9-6x+x^2\right) = \\ = 324x -\cancel{216x^2}+36x^3+ \cancel{216x^2}-144x^3+ \cancel{24x^4}+36x^3 -\cancel{24x^4}+4x^5 $$ |
| ② | Combine like terms: $$ 324x \, \color{blue}{ -\cancel{216x^2}} \,+ \color{green}{36x^3} + \, \color{blue}{ \cancel{216x^2}} \, \color{orange}{-144x^3} + \, \color{blue}{ \cancel{24x^4}} \,+ \color{orange}{36x^3} \, \color{blue}{ -\cancel{24x^4}} \,+4x^5 = 4x^5 \color{orange}{-72x^3} +324x $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(4x^5-72x^3+324x \right) = -4x^5+72x^3-324x $$ |
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