Question
Answer
$$2(x-1)(x+3)(x+2)=2x^3+8x^2+2x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-1)(x+3)(x+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x-2)(x+3)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2+6x-2x-6)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(2x^2+4x-6)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3+4x^2+4x^2+8x-6x-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2x^3+8x^2+2x-12\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( x-1\right) $ $$ \color{blue}{2} \cdot \left( x-1\right) = 2x-2 $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x-2}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{2x-2}\right) \cdot \left( x+3\right) = 2x^2+6x-2x-6 $$ |
| ③ | Combine like terms: $$ 2x^2+ \color{blue}{6x} \color{blue}{-2x} -6 = 2x^2+ \color{blue}{4x} -6 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{2x^2+4x-6}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{2x^2+4x-6}\right) \cdot \left( x+2\right) = 2x^3+4x^2+4x^2+8x-6x-12 $$ |
| ⑤ | Combine like terms: $$ 2x^3+ \color{blue}{4x^2} + \color{blue}{4x^2} + \color{red}{8x} \color{red}{-6x} -12 = 2x^3+ \color{blue}{8x^2} + \color{red}{2x} -12 $$ |
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