Answer
$$8p(p^2+7p-2)-(9p^3-2p^2)=-p^3+58p^2-16p$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}8p(p^2+7p-2)-(9p^3-2p^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8p^3+56p^2-16p-(9p^3-2p^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8p^3+56p^2-16p-9p^3+2p^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-p^3+58p^2-16p\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{8p} $ by $ \left( p^2+7p-2\right) $ $$ \color{blue}{8p} \cdot \left( p^2+7p-2\right) = 8p^3+56p^2-16p $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9p^3-2p^2 \right) = -9p^3+2p^2 $$ |
| ③ | Combine like terms: $$ \color{blue}{8p^3} + \color{red}{56p^2} -16p \color{blue}{-9p^3} + \color{red}{2p^2} = \color{blue}{-p^3} + \color{red}{58p^2} -16p $$ |
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