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