Answer
$$2(g^3+2g)-4g(g^2+5)=-2g^3-16g$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(g^3+2g)-4g(g^2+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2g^3+4g-(4g^3+20g) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2g^3+4g-4g^3-20g \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2g^3-16g\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( g^3+2g\right) $ $$ \color{blue}{2} \cdot \left( g^3+2g\right) = 2g^3+4g $$Multiply $ \color{blue}{4g} $ by $ \left( g^2+5\right) $ $$ \color{blue}{4g} \cdot \left( g^2+5\right) = 4g^3+20g $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4g^3+20g \right) = -4g^3-20g $$ |
| ③ | Combine like terms: $$ \color{blue}{2g^3} + \color{red}{4g} \color{blue}{-4g^3} \color{red}{-20g} = \color{blue}{-2g^3} \color{red}{-16g} $$ |
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