Answer
$$2x(x-2)(x+3)(x+4)=2x^4+10x^3-4x^2-48x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2x(x-2)(x+3)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2-4x)(x+3)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^3+6x^2-4x^2-12x)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(2x^3+2x^2-12x)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^4+8x^3+2x^3+8x^2-12x^2-48x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2x^4+10x^3-4x^2-48x\end{aligned} $$ | |
| 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 | Multiply each term of $ \left( \color{blue}{2x^3+2x^2-12x}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{2x^3+2x^2-12x}\right) \cdot \left( x+4\right) = 2x^4+8x^3+2x^3+8x^2-12x^2-48x $$ |
| ⑤ | Combine like terms: $$ 2x^4+ \color{blue}{8x^3} + \color{blue}{2x^3} + \color{red}{8x^2} \color{red}{-12x^2} -48x = 2x^4+ \color{blue}{10x^3} \color{red}{-4x^2} -48x $$ |
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