Question
Answer
$$x\cdot2-2x(x-2)(x+3)=-2x^3-2x^2+14x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x\cdot2-2x(x-2)(x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x\cdot2-(2x^2-4x)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x\cdot2-(2x^3+6x^2-4x^2-12x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x\cdot2-(2x^3+2x^2-12x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x-2x^3-2x^2+12x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-2x^3-2x^2+14x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2x} $ by $ \left( x-2\right) $ $$ \color{blue}{2x} \cdot \left( x-2\right) = 2x^2-4x $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x^2-4x}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{2x^2-4x}\right) \cdot \left( x+3\right) = 2x^3+6x^2-4x^2-12x $$ |
| ③ | Combine like terms: $$ 2x^3+ \color{blue}{6x^2} \color{blue}{-4x^2} -12x = 2x^3+ \color{blue}{2x^2} -12x $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x^3+2x^2-12x \right) = -2x^3-2x^2+12x $$ |
| ⑤ | Combine like terms: $$ \color{blue}{2x} -2x^3-2x^2+ \color{blue}{12x} = -2x^3-2x^2+ \color{blue}{14x} $$ |
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