Answer
$$(6c-2)(4c+2)-(c+7)=24c^2+3c-11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6c-2)(4c+2)-(c+7)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}24c^2+12c-8c-4-(c+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}24c^2+4c-4-(c+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}24c^2+4c-4-c-7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}24c^2+3c-11\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6c-2}\right) $ by each term in $ \left( 4c+2\right) $. $$ \left( \color{blue}{6c-2}\right) \cdot \left( 4c+2\right) = 24c^2+12c-8c-4 $$ |
| ② | Combine like terms: $$ 24c^2+ \color{blue}{12c} \color{blue}{-8c} -4 = 24c^2+ \color{blue}{4c} -4 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( c+7 \right) = -c-7 $$ |
| ④ | Combine like terms: $$ 24c^2+ \color{blue}{4c} \color{red}{-4} \color{blue}{-c} \color{red}{-7} = 24c^2+ \color{blue}{3c} \color{red}{-11} $$ |
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