Answer
$$5k-6(2k-3\cdot(2-k)-7k)=17k+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5k-6(2k-3\cdot(2-k)-7k)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5k-6(2k-(6-3k)-7k) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5k-6(2k-6+3k-7k) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5k-6(-2k-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5k-(-12k-36) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}5k+12k+36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}17k+36\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 2-k\right) $ $$ \color{blue}{3} \cdot \left( 2-k\right) = 6-3k $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6-3k \right) = -6+3k $$ |
| ③ | Combine like terms: $$ \color{blue}{2k} -6+ \color{red}{3k} \color{red}{-7k} = \color{red}{-2k} -6 $$ |
| ④ | Multiply $ \color{blue}{6} $ by $ \left( -2k-6\right) $ $$ \color{blue}{6} \cdot \left( -2k-6\right) = -12k-36 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -12k-36 \right) = 12k+36 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{5k} + \color{blue}{12k} +36 = \color{blue}{17k} +36 $$ |
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