Answer
$$(6-2x-x^2)^2=x^4+4x^3-8x^2-24x+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6-2x-x^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4+4x^3-8x^2-24x+36\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6-2x-x^2}\right) $ by each term in $ \left( 6-2x-x^2\right) $. $$ \left( \color{blue}{6-2x-x^2}\right) \cdot \left( 6-2x-x^2\right) = 36-12x-6x^2-12x+4x^2+2x^3-6x^2+2x^3+x^4 $$ |
| ② | Combine like terms: $$ 36 \color{blue}{-12x} \color{red}{-6x^2} \color{blue}{-12x} + \color{green}{4x^2} + \color{orange}{2x^3} \color{green}{-6x^2} + \color{orange}{2x^3} +x^4 = \\ = x^4+ \color{orange}{4x^3} \color{green}{-8x^2} \color{blue}{-24x} +36 $$ |
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