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