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