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