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