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