Answer
$$2(x-3)\cdot2-4(x-3)+8=8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-3)\cdot2-4(x-3)+8& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x-6)\cdot2-(4x-12)+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x-12-(4x-12)+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x-12-4x+12+8 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{4x} -\cancel{12} -\cancel{4x}+ \cancel{12}+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}8\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( x-3\right) $ $$ \color{blue}{2} \cdot \left( x-3\right) = 2x-6 $$Multiply $ \color{blue}{4} $ by $ \left( x-3\right) $ $$ \color{blue}{4} \cdot \left( x-3\right) = 4x-12 $$ |
| ② | $$ \left( \color{blue}{2x-6}\right) \cdot 2 = 4x-12 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4x-12 \right) = -4x+12 $$ |
| ④ | Combine like terms: $$ \, \color{blue}{ \cancel{4x}} \, \, \color{green}{ -\cancel{12}} \, \, \color{blue}{ -\cancel{4x}} \,+ \, \color{blue}{ \cancel{12}} \,+ \color{blue}{8} = \color{blue}{8} $$ |
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