Answer
$$(x-2)(5x^5+4x^4+3x^3+2x^2+x+1)=5x^6-6x^5-5x^4-4x^3-3x^2-x-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(5x^5+4x^4+3x^3+2x^2+x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5x^6-6x^5-5x^4-4x^3-3x^2-x-2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( 5x^5+4x^4+3x^3+2x^2+x+1\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( 5x^5+4x^4+3x^3+2x^2+x+1\right) = \\ = 5x^6+4x^5+3x^4+2x^3+x^2+x-10x^5-8x^4-6x^3-4x^2-2x-2 $$ |
| ② | Combine like terms: $$ 5x^6+ \color{blue}{4x^5} + \color{red}{3x^4} + \color{green}{2x^3} + \color{orange}{x^2} + \color{blue}{x} \color{blue}{-10x^5} \color{red}{-8x^4} \color{green}{-6x^3} \color{orange}{-4x^2} \color{blue}{-2x} -2 = \\ = 5x^6 \color{blue}{-6x^5} \color{red}{-5x^4} \color{green}{-4x^3} \color{orange}{-3x^2} \color{blue}{-x} -2 $$ |
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