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