Answer
$$2(4x-3x^3)-3(3x^3+4x^2)=-15x^3-12x^2+8x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(4x-3x^3)-3(3x^3+4x^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8x-6x^3-(9x^3+12x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8x-6x^3-9x^3-12x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-15x^3-12x^2+8x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 4x-3x^3\right) $ $$ \color{blue}{2} \cdot \left( 4x-3x^3\right) = 8x-6x^3 $$Multiply $ \color{blue}{3} $ by $ \left( 3x^3+4x^2\right) $ $$ \color{blue}{3} \cdot \left( 3x^3+4x^2\right) = 9x^3+12x^2 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9x^3+12x^2 \right) = -9x^3-12x^2 $$ |
| ③ | Combine like terms: $$ 8x \color{blue}{-6x^3} \color{blue}{-9x^3} -12x^2 = \color{blue}{-15x^3} -12x^2+8x $$ |
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