Question
Answer
$$(-x^2+x+2)^2=x^4-2x^3-3x^2+4x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-x^2+x+2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4-2x^3-3x^2+4x+4\end{aligned} $$ | |
| 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: $$ x^4 \color{blue}{-x^3} \color{red}{-2x^2} \color{blue}{-x^3} + \color{green}{x^2} + \color{orange}{2x} \color{green}{-2x^2} + \color{orange}{2x} +4 = x^4 \color{blue}{-2x^3} \color{green}{-3x^2} + \color{orange}{4x} +4 $$ |
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