Answer
$$2(a-3b)-(-3b(5a+2b))=15ab+6b^2+2a-6b$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(a-3b)-(-3b(5a+2b))& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2a-6b-(-(15ab+6b^2)) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2a-6b-(-15ab-6b^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2a-6b+15ab+6b^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}15ab+6b^2+2a-6b\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( a-3b\right) $ $$ \color{blue}{2} \cdot \left( a-3b\right) = 2a-6b $$Multiply $ \color{blue}{3b} $ by $ \left( 5a+2b\right) $ $$ \color{blue}{3b} \cdot \left( 5a+2b\right) = 15ab+6b^2 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(15ab+6b^2 \right) = -15ab-6b^2 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -15ab-6b^2 \right) = 15ab+6b^2 $$ |
| ④ | Combine like terms: $$ 15ab+6b^2+2a-6b = 15ab+6b^2+2a-6b $$ |
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