Tap the blue circles to see an explanation.
$$ \begin{aligned}(110a-10b+10c)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}12100a^2-2200ab+2200ac+100b^2-200bc+100c^2\end{aligned} $$ | |
① | Multiply each term of $ \left( \color{blue}{110a-10b+10c}\right) $ by each term in $ \left( 110a-10b+10c\right) $. $$ \left( \color{blue}{110a-10b+10c}\right) \cdot \left( 110a-10b+10c\right) = \\ = 12100a^2-1100ab+1100ac-1100ab+100b^2-100bc+1100ac-100bc+100c^2 $$ |
② | Combine like terms: $$ 12100a^2 \color{blue}{-1100ab} + \color{red}{1100ac} \color{blue}{-1100ab} +100b^2 \color{green}{-100bc} + \color{red}{1100ac} \color{green}{-100bc} +100c^2 = \\ = 12100a^2 \color{blue}{-2200ab} + \color{red}{2200ac} +100b^2 \color{green}{-200bc} +100c^2 $$ |