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