Answer
$$(x^2-2x-2)(x^2-5x+1)=x^4-7x^3+9x^2+8x-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-2x-2)(x^2-5x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4-7x^3+9x^2+8x-2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-2x-2}\right) $ by each term in $ \left( x^2-5x+1\right) $. $$ \left( \color{blue}{x^2-2x-2}\right) \cdot \left( x^2-5x+1\right) = x^4-5x^3+x^2-2x^3+10x^2-2x-2x^2+10x-2 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-5x^3} + \color{red}{x^2} \color{blue}{-2x^3} + \color{green}{10x^2} \color{orange}{-2x} \color{green}{-2x^2} + \color{orange}{10x} -2 = x^4 \color{blue}{-7x^3} + \color{green}{9x^2} + \color{orange}{8x} -2 $$ |
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