Answer
$$(2x-1)(x-3)(x+4)=2x^3+x^2-25x+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-1)(x-3)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2-6x-x+3)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-7x+3)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+8x^2-7x^2-28x+3x+12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3+x^2-25x+12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x-1}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{2x-1}\right) \cdot \left( x-3\right) = 2x^2-6x-x+3 $$ |
| ② | Combine like terms: $$ 2x^2 \color{blue}{-6x} \color{blue}{-x} +3 = 2x^2 \color{blue}{-7x} +3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-7x+3}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{2x^2-7x+3}\right) \cdot \left( x+4\right) = 2x^3+8x^2-7x^2-28x+3x+12 $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{8x^2} \color{blue}{-7x^2} \color{red}{-28x} + \color{red}{3x} +12 = 2x^3+ \color{blue}{x^2} \color{red}{-25x} +12 $$ |
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