Question
Answer
$$(x^4+x^2y^2+y^4)(x^2-2xy+y^2)=x^6-2x^5y+2x^4y^2-2x^3y^3+2x^2y^4-2xy^5+y^6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^4+x^2y^2+y^4)(x^2-2xy+y^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^6-2x^5y+2x^4y^2-2x^3y^3+2x^2y^4-2xy^5+y^6\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^4+x^2y^2+y^4}\right) $ by each term in $ \left( x^2-2xy+y^2\right) $. $$ \left( \color{blue}{x^4+x^2y^2+y^4}\right) \cdot \left( x^2-2xy+y^2\right) = \\ = x^6-2x^5y+x^4y^2+x^4y^2-2x^3y^3+x^2y^4+x^2y^4-2xy^5+y^6 $$ |
| ② | Combine like terms: $$ x^6-2x^5y+ \color{blue}{x^4y^2} + \color{blue}{x^4y^2} -2x^3y^3+ \color{red}{x^2y^4} + \color{red}{x^2y^4} -2xy^5+y^6 = \\ = x^6-2x^5y+ \color{blue}{2x^4y^2} -2x^3y^3+ \color{red}{2x^2y^4} -2xy^5+y^6 $$ |
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