Answer
$$(-x^2-6x+5)(-6x^3+8x^2+9x+3)=6x^5+28x^4-87x^3-17x^2+27x+15$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-x^2-6x+5)(-6x^3+8x^2+9x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x^5+28x^4-87x^3-17x^2+27x+15\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-x^2-6x+5}\right) $ by each term in $ \left( -6x^3+8x^2+9x+3\right) $. $$ \left( \color{blue}{-x^2-6x+5}\right) \cdot \left( -6x^3+8x^2+9x+3\right) = \\ = 6x^5-8x^4-9x^3-3x^2+36x^4-48x^3-54x^2-18x-30x^3+40x^2+45x+15 $$ |
| ② | Combine like terms: $$ 6x^5 \color{blue}{-8x^4} \color{red}{-9x^3} \color{green}{-3x^2} + \color{blue}{36x^4} \color{orange}{-48x^3} \color{blue}{-54x^2} \color{red}{-18x} \color{orange}{-30x^3} + \color{blue}{40x^2} + \color{red}{45x} +15 = \\ = 6x^5+ \color{blue}{28x^4} \color{orange}{-87x^3} \color{blue}{-17x^2} + \color{red}{27x} +15 $$ |
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