Question
Answer
$$(x^2-4x+2)^2=x^4-8x^3+20x^2-16x+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-4x+2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4-8x^3+20x^2-16x+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-4x+2}\right) $ by each term in $ \left( x^2-4x+2\right) $. $$ \left( \color{blue}{x^2-4x+2}\right) \cdot \left( x^2-4x+2\right) = x^4-4x^3+2x^2-4x^3+16x^2-8x+2x^2-8x+4 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-4x^3} + \color{red}{2x^2} \color{blue}{-4x^3} + \color{green}{16x^2} \color{orange}{-8x} + \color{green}{2x^2} \color{orange}{-8x} +4 = \\ = x^4 \color{blue}{-8x^3} + \color{green}{20x^2} \color{orange}{-16x} +4 $$ |
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