Question
Answer
$$(6-a-3b-2c)^2=a^2+6ab+4ac+9b^2+12bc+4c^2-12a-36b-24c+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6-a-3b-2c)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^2+6ab+4ac+9b^2+12bc+4c^2-12a-36b-24c+36\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6-a-3b-2c}\right) $ by each term in $ \left( 6-a-3b-2c\right) $. $$ \left( \color{blue}{6-a-3b-2c}\right) \cdot \left( 6-a-3b-2c\right) = \\ = 36-6a-18b-12c-6a+a^2+3ab+2ac-18b+3ab+9b^2+6bc-12c+2ac+6bc+4c^2 $$ |
| ② | Combine like terms: $$ 36 \color{blue}{-6a} \color{red}{-18b} \color{green}{-12c} \color{blue}{-6a} +a^2+ \color{orange}{3ab} + \color{blue}{2ac} \color{red}{-18b} + \color{orange}{3ab} +9b^2+ \color{red}{6bc} \color{green}{-12c} + \color{blue}{2ac} + \color{red}{6bc} +4c^2 = \\ = a^2+ \color{orange}{6ab} + \color{blue}{4ac} +9b^2+ \color{red}{12bc} +4c^2 \color{blue}{-12a} \color{red}{-36b} \color{green}{-24c} +36 $$ |
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