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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