Question
Answer
$$2(2a+b)-3(3a-2b)=-5a+8b$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(2a+b)-3(3a-2b)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4a+2b-(9a-6b) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4a+2b-9a+6b \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-5a+8b\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 2a+b\right) $ $$ \color{blue}{2} \cdot \left( 2a+b\right) = 4a+2b $$Multiply $ \color{blue}{3} $ by $ \left( 3a-2b\right) $ $$ \color{blue}{3} \cdot \left( 3a-2b\right) = 9a-6b $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9a-6b \right) = -9a+6b $$ |
| ③ | Combine like terms: $$ \color{blue}{4a} + \color{red}{2b} \color{blue}{-9a} + \color{red}{6b} = \color{blue}{-5a} + \color{red}{8b} $$ |
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