Question
Answer
$$(1+5x+10x^2+10x^3+5x^4+x^5)(x+2)=x^6+7x^5+20x^4+30x^3+25x^2+11x+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+5x+10x^2+10x^3+5x^4+x^5)(x+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^6+7x^5+20x^4+30x^3+25x^2+11x+2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1+5x+10x^2+10x^3+5x^4+x^5}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{1+5x+10x^2+10x^3+5x^4+x^5}\right) \cdot \left( x+2\right) = \\ = x+2+5x^2+10x+10x^3+20x^2+10x^4+20x^3+5x^5+10x^4+x^6+2x^5 $$ |
| ② | Combine like terms: $$ \color{blue}{x} +2+ \color{red}{5x^2} + \color{blue}{10x} + \color{green}{10x^3} + \color{red}{20x^2} + \color{orange}{10x^4} + \color{green}{20x^3} + \color{blue}{5x^5} + \color{orange}{10x^4} +x^6+ \color{blue}{2x^5} = \\ = x^6+ \color{blue}{7x^5} + \color{orange}{20x^4} + \color{green}{30x^3} + \color{red}{25x^2} + \color{blue}{11x} +2 $$ |
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