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