Answer
$$(1-3x+2x^2)(5+4x-x^2)=-2x^4+11x^3-3x^2-11x+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1-3x+2x^2)(5+4x-x^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2x^4+11x^3-3x^2-11x+5\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1-3x+2x^2}\right) $ by each term in $ \left( 5+4x-x^2\right) $. $$ \left( \color{blue}{1-3x+2x^2}\right) \cdot \left( 5+4x-x^2\right) = 5+4x-x^2-15x-12x^2+3x^3+10x^2+8x^3-2x^4 $$ |
| ② | Combine like terms: $$ 5+ \color{blue}{4x} \color{red}{-x^2} \color{blue}{-15x} \color{green}{-12x^2} + \color{orange}{3x^3} + \color{green}{10x^2} + \color{orange}{8x^3} -2x^4 = \\ = -2x^4+ \color{orange}{11x^3} \color{green}{-3x^2} \color{blue}{-11x} +5 $$ |
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