Answer
$$(ab+cd+1)^2=a^2b^2+2abcd+c^2d^2+2ab+2cd+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(ab+cd+1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^2b^2+2abcd+c^2d^2+2ab+2cd+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{ab+cd+1}\right) $ by each term in $ \left( ab+cd+1\right) $. $$ \left( \color{blue}{ab+cd+1}\right) \cdot \left( ab+cd+1\right) = a^2b^2+abcd+ab+abcd+c^2d^2+cd+ab+cd+1 $$ |
| ② | Combine like terms: $$ a^2b^2+ \color{blue}{abcd} + \color{red}{ab} + \color{blue}{abcd} +c^2d^2+ \color{green}{cd} + \color{red}{ab} + \color{green}{cd} +1 = \\ = a^2b^2+ \color{blue}{2abcd} +c^2d^2+ \color{red}{2ab} + \color{green}{2cd} +1 $$ |
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