Question
Answer
$$(-x^2+11x-1)(2x^2-5x+5)=-2x^4+27x^3-62x^2+60x-5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-x^2+11x-1)(2x^2-5x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2x^4+27x^3-62x^2+60x-5\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-x^2+11x-1}\right) $ by each term in $ \left( 2x^2-5x+5\right) $. $$ \left( \color{blue}{-x^2+11x-1}\right) \cdot \left( 2x^2-5x+5\right) = -2x^4+5x^3-5x^2+22x^3-55x^2+55x-2x^2+5x-5 $$ |
| ② | Combine like terms: $$ -2x^4+ \color{blue}{5x^3} \color{red}{-5x^2} + \color{blue}{22x^3} \color{green}{-55x^2} + \color{orange}{55x} \color{green}{-2x^2} + \color{orange}{5x} -5 = \\ = -2x^4+ \color{blue}{27x^3} \color{green}{-62x^2} + \color{orange}{60x} -5 $$ |
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