Question
Answer
$$a(b-c)+b(c-a)+c(a-b)=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}a(b-c)+b(c-a)+c(a-b)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}ab-ac+bc-ab+ac-bc \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-ac+bc+ac-bc \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}0\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{a} $ by $ \left( b-c\right) $ $$ \color{blue}{a} \cdot \left( b-c\right) = ab-ac $$Multiply $ \color{blue}{b} $ by $ \left( c-a\right) $ $$ \color{blue}{b} \cdot \left( c-a\right) = bc-ab $$Multiply $ \color{blue}{c} $ by $ \left( a-b\right) $ $$ \color{blue}{c} \cdot \left( a-b\right) = ac-bc $$ |
| ② | Combine like terms: $$ \, \color{blue}{ \cancel{ab}} \,-ac+bc \, \color{blue}{ -\cancel{ab}} \, = -ac+bc $$ |
| ③ | Combine like terms: $$ \, \color{blue}{ -\cancel{ac}} \,+ \, \color{green}{ \cancel{bc}} \,+ \, \color{blue}{ \cancel{ac}} \, \, \color{green}{ -\cancel{bc}} \, = 0 $$ |
This page was created using
Simplify polynomials calculator