Question
Answer
$$(3x^2-7x+1)(-3x^3+2x-3)=-9x^5+21x^4+3x^3-23x^2+23x-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x^2-7x+1)(-3x^3+2x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-9x^5+21x^4+3x^3-23x^2+23x-3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3x^2-7x+1}\right) $ by each term in $ \left( -3x^3+2x-3\right) $. $$ \left( \color{blue}{3x^2-7x+1}\right) \cdot \left( -3x^3+2x-3\right) = -9x^5+6x^3-9x^2+21x^4-14x^2+21x-3x^3+2x-3 $$ |
| ② | Combine like terms: $$ -9x^5+ \color{blue}{6x^3} \color{red}{-9x^2} +21x^4 \color{red}{-14x^2} + \color{green}{21x} \color{blue}{-3x^3} + \color{green}{2x} -3 = \\ = -9x^5+21x^4+ \color{blue}{3x^3} \color{red}{-23x^2} + \color{green}{23x} -3 $$ |
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