Answer
$$(x-3)(2x+1)(x-1)(x+4)=2x^4+x^3-26x^2+11x+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-3)(2x+1)(x-1)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2+x-6x-3)(x-1)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-5x-3)(x-1)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(2x^3-2x^2-5x^2+5x-3x+3)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(2x^3-7x^2+2x+3)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}2x^4+x^3-26x^2+11x+12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-3}\right) $ by each term in $ \left( 2x+1\right) $. $$ \left( \color{blue}{x-3}\right) \cdot \left( 2x+1\right) = 2x^2+x-6x-3 $$ |
| ② | Combine like terms: $$ 2x^2+ \color{blue}{x} \color{blue}{-6x} -3 = 2x^2 \color{blue}{-5x} -3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-5x-3}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{2x^2-5x-3}\right) \cdot \left( x-1\right) = 2x^3-2x^2-5x^2+5x-3x+3 $$ |
| ④ | Combine like terms: $$ 2x^3 \color{blue}{-2x^2} \color{blue}{-5x^2} + \color{red}{5x} \color{red}{-3x} +3 = 2x^3 \color{blue}{-7x^2} + \color{red}{2x} +3 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{2x^3-7x^2+2x+3}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{2x^3-7x^2+2x+3}\right) \cdot \left( x+4\right) = 2x^4+8x^3-7x^3-28x^2+2x^2+8x+3x+12 $$ |
| ⑥ | Combine like terms: $$ 2x^4+ \color{blue}{8x^3} \color{blue}{-7x^3} \color{red}{-28x^2} + \color{red}{2x^2} + \color{green}{8x} + \color{green}{3x} +12 = 2x^4+ \color{blue}{x^3} \color{red}{-26x^2} + \color{green}{11x} +12 $$ |
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