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