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