Answer
$$a+b-c+a+b+2c-(a+b+c)=a+b$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}a+b-c+a+b+2c-(a+b+c)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2a+2b+c-(a+b+c) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2a+2b+c-a-b-c \xlongequal{ } \\[1 em] & \xlongequal{ }2a+2b+ \cancel{c}-a-b -\cancel{c} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}a+b\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{a} + \color{red}{b} \color{green}{-c} + \color{blue}{a} + \color{red}{b} + \color{green}{2c} = \color{blue}{2a} + \color{red}{2b} + \color{green}{c} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( a+b+c \right) = -a-b-c $$ |
| ③ | Combine like terms: $$ \color{blue}{2a} + \color{red}{2b} + \, \color{green}{ \cancel{c}} \, \color{blue}{-a} \color{red}{-b} \, \color{green}{ -\cancel{c}} \, = \color{blue}{a} + \color{red}{b} $$ |
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