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