Question
Answer
$$3x(2x+1)+x(-3x-2)-4x(x+6)=-x^2-23x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3x(2x+1)+x(-3x-2)-4x(x+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6x^2+3x-3x^2-2x-(4x^2+24x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^2+x-(4x^2+24x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^2+x-4x^2-24x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-x^2-23x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3x} $ by $ \left( 2x+1\right) $ $$ \color{blue}{3x} \cdot \left( 2x+1\right) = 6x^2+3x $$Multiply $ \color{blue}{x} $ by $ \left( -3x-2\right) $ $$ \color{blue}{x} \cdot \left( -3x-2\right) = -3x^2-2x $$Multiply $ \color{blue}{4x} $ by $ \left( x+6\right) $ $$ \color{blue}{4x} \cdot \left( x+6\right) = 4x^2+24x $$ |
| ② | Combine like terms: $$ \color{blue}{6x^2} + \color{red}{3x} \color{blue}{-3x^2} \color{red}{-2x} = \color{blue}{3x^2} + \color{red}{x} $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4x^2+24x \right) = -4x^2-24x $$ |
| ④ | Combine like terms: $$ \color{blue}{3x^2} + \color{red}{x} \color{blue}{-4x^2} \color{red}{-24x} = \color{blue}{-x^2} \color{red}{-23x} $$ |
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