Question
Answer
$$2(x^2+xy+y^2)^2=2x^4+4x^3y+6x^2y^2+4xy^3+2y^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x^2+xy+y^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2(x^4+2x^3y+3x^2y^2+2xy^3+y^4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^4+4x^3y+6x^2y^2+4xy^3+2y^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+xy+y^2}\right) $ by each term in $ \left( x^2+xy+y^2\right) $. $$ \left( \color{blue}{x^2+xy+y^2}\right) \cdot \left( x^2+xy+y^2\right) = x^4+x^3y+x^2y^2+x^3y+x^2y^2+xy^3+x^2y^2+xy^3+y^4 $$ |
| ② | Combine like terms: $$ x^4+ \color{blue}{x^3y} + \color{red}{x^2y^2} + \color{blue}{x^3y} + \color{green}{x^2y^2} + \color{orange}{xy^3} + \color{green}{x^2y^2} + \color{orange}{xy^3} +y^4 = \\ = x^4+ \color{blue}{2x^3y} + \color{green}{3x^2y^2} + \color{orange}{2xy^3} +y^4 $$ |
| ③ | Multiply $ \color{blue}{2} $ by $ \left( x^4+2x^3y+3x^2y^2+2xy^3+y^4\right) $ $$ \color{blue}{2} \cdot \left( x^4+2x^3y+3x^2y^2+2xy^3+y^4\right) = 2x^4+4x^3y+6x^2y^2+4xy^3+2y^4 $$ |
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