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