Answer
$$(2c-5)(c+6)+(c+6)(3c-2)=5c^2+23c-42$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2c-5)(c+6)+(c+6)(3c-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2c^2+12c-5c-30+3c^2-2c+18c-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2c^2+7c-30+3c^2+16c-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5c^2+23c-42\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2c-5}\right) $ by each term in $ \left( c+6\right) $. $$ \left( \color{blue}{2c-5}\right) \cdot \left( c+6\right) = 2c^2+12c-5c-30 $$Multiply each term of $ \left( \color{blue}{c+6}\right) $ by each term in $ \left( 3c-2\right) $. $$ \left( \color{blue}{c+6}\right) \cdot \left( 3c-2\right) = 3c^2-2c+18c-12 $$ |
| ② | Combine like terms: $$ 2c^2+ \color{blue}{12c} \color{blue}{-5c} -30 = 2c^2+ \color{blue}{7c} -30 $$Combine like terms: $$ 3c^2 \color{blue}{-2c} + \color{blue}{18c} -12 = 3c^2+ \color{blue}{16c} -12 $$ |
| ③ | Combine like terms: $$ \color{blue}{2c^2} + \color{red}{7c} \color{green}{-30} + \color{blue}{3c^2} + \color{red}{16c} \color{green}{-12} = \color{blue}{5c^2} + \color{red}{23c} \color{green}{-42} $$ |
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