Answer
$$-5x^2\cdot(3+x)-3(-x^3+5x^2+x)+2x^3=-30x^2-3x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-5x^2\cdot(3+x)-3(-x^3+5x^2+x)+2x^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(15x^2+5x^3)-(-3x^3+15x^2+3x)+2x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-15x^2-5x^3-(-3x^3+15x^2+3x)+2x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-15x^2-5x^3+3x^3-15x^2-3x+2x^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-30x^2-3x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{5x^2} $ by $ \left( 3+x\right) $ $$ \color{blue}{5x^2} \cdot \left( 3+x\right) = 15x^2+5x^3 $$Multiply $ \color{blue}{3} $ by $ \left( -x^3+5x^2+x\right) $ $$ \color{blue}{3} \cdot \left( -x^3+5x^2+x\right) = -3x^3+15x^2+3x $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(15x^2+5x^3 \right) = -15x^2-5x^3 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -3x^3+15x^2+3x \right) = 3x^3-15x^2-3x $$ |
| ④ | Combine like terms: $$ \color{blue}{-15x^2} \color{red}{-5x^3} + \color{green}{3x^3} \color{blue}{-15x^2} -3x+ \color{green}{2x^3} = \color{blue}{-30x^2} -3x $$ |
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