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