Question
Answer
$$(x+2x^2-x^3-x^4)^2=x^8+2x^7-3x^6-6x^5+2x^4+4x^3+x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2x^2-x^3-x^4)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^8+2x^7-3x^6-6x^5+2x^4+4x^3+x^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+2x^2-x^3-x^4}\right) $ by each term in $ \left( x+2x^2-x^3-x^4\right) $. $$ \left( \color{blue}{x+2x^2-x^3-x^4}\right) \cdot \left( x+2x^2-x^3-x^4\right) = \\ = x^2+2x^3-x^4-x^5+2x^3+4x^4-2x^5-2x^6-x^4-2x^5+x^6+x^7-x^5-2x^6+x^7+x^8 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{2x^3} \color{red}{-x^4} \color{green}{-x^5} + \color{blue}{2x^3} + \color{orange}{4x^4} \color{blue}{-2x^5} \color{red}{-2x^6} \color{orange}{-x^4} \color{green}{-2x^5} + \color{orange}{x^6} + \color{blue}{x^7} \color{green}{-x^5} \color{orange}{-2x^6} + \color{blue}{x^7} +x^8 = \\ = x^8+ \color{blue}{2x^7} \color{orange}{-3x^6} \color{green}{-6x^5} + \color{orange}{2x^4} + \color{blue}{4x^3} +x^2 $$ |
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