Question
Answer
$$(4-a-b-2c)^2=a^2+2ab+4ac+b^2+4bc+4c^2-8a-8b-16c+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-a-b-2c)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^2+2ab+4ac+b^2+4bc+4c^2-8a-8b-16c+16\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4-a-b-2c}\right) $ by each term in $ \left( 4-a-b-2c\right) $. $$ \left( \color{blue}{4-a-b-2c}\right) \cdot \left( 4-a-b-2c\right) = \\ = 16-4a-4b-8c-4a+a^2+ab+2ac-4b+ab+b^2+2bc-8c+2ac+2bc+4c^2 $$ |
| ② | Combine like terms: $$ 16 \color{blue}{-4a} \color{red}{-4b} \color{green}{-8c} \color{blue}{-4a} +a^2+ \color{orange}{ab} + \color{blue}{2ac} \color{red}{-4b} + \color{orange}{ab} +b^2+ \color{red}{2bc} \color{green}{-8c} + \color{blue}{2ac} + \color{red}{2bc} +4c^2 = \\ = a^2+ \color{orange}{2ab} + \color{blue}{4ac} +b^2+ \color{red}{4bc} +4c^2 \color{blue}{-8a} \color{red}{-8b} \color{green}{-16c} +16 $$ |
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