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