Answer
$$(4x-1)(-x^2+6x+9)=-4x^3+25x^2+30x-9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x-1)(-x^2+6x+9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-4x^3+24x^2+36x+x^2-6x-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4x^3+25x^2+30x-9\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4x-1}\right) $ by each term in $ \left( -x^2+6x+9\right) $. $$ \left( \color{blue}{4x-1}\right) \cdot \left( -x^2+6x+9\right) = -4x^3+24x^2+36x+x^2-6x-9 $$ |
| ② | Combine like terms: $$ -4x^3+ \color{blue}{24x^2} + \color{red}{36x} + \color{blue}{x^2} \color{red}{-6x} -9 = -4x^3+ \color{blue}{25x^2} + \color{red}{30x} -9 $$ |
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