Answer
$$(-12^3-3x^2+11x)(3x^3-x^2+3x)=-9x^5+36x^4-5204x^3+1761x^2-5184x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-12^3-3x^2+11x)(3x^3-x^2+3x)& \xlongequal{ }(-1728-3x^2+11x)(3x^3-x^2+3x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-9x^5+36x^4-5204x^3+1761x^2-5184x\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-1728-3x^2+11x}\right) $ by each term in $ \left( 3x^3-x^2+3x\right) $. $$ \left( \color{blue}{-1728-3x^2+11x}\right) \cdot \left( 3x^3-x^2+3x\right) = \\ = -5184x^3+1728x^2-5184x-9x^5+3x^4-9x^3+33x^4-11x^3+33x^2 $$ |
| ② | Combine like terms: $$ \color{blue}{-5184x^3} + \color{red}{1728x^2} -5184x-9x^5+ \color{green}{3x^4} \color{orange}{-9x^3} + \color{green}{33x^4} \color{orange}{-11x^3} + \color{red}{33x^2} = \\ = -9x^5+ \color{green}{36x^4} \color{orange}{-5204x^3} + \color{red}{1761x^2} -5184x $$ |
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