Question
Answer
$$(2-a-3b-5c)^2=a^2+6ab+10ac+9b^2+30bc+25c^2-4a-12b-20c+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2-a-3b-5c)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^2+6ab+10ac+9b^2+30bc+25c^2-4a-12b-20c+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2-a-3b-5c}\right) $ by each term in $ \left( 2-a-3b-5c\right) $. $$ \left( \color{blue}{2-a-3b-5c}\right) \cdot \left( 2-a-3b-5c\right) = \\ = 4-2a-6b-10c-2a+a^2+3ab+5ac-6b+3ab+9b^2+15bc-10c+5ac+15bc+25c^2 $$ |
| ② | Combine like terms: $$ 4 \color{blue}{-2a} \color{red}{-6b} \color{green}{-10c} \color{blue}{-2a} +a^2+ \color{orange}{3ab} + \color{blue}{5ac} \color{red}{-6b} + \color{orange}{3ab} +9b^2+ \color{red}{15bc} \color{green}{-10c} + \color{blue}{5ac} + \color{red}{15bc} +25c^2 = \\ = a^2+ \color{orange}{6ab} + \color{blue}{10ac} +9b^2+ \color{red}{30bc} +25c^2 \color{blue}{-4a} \color{red}{-12b} \color{green}{-20c} +4 $$ |
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