Answer
$$(x-2)(x^2+4)(2x+3)=2x^4-x^3+2x^2-4x-24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x^2+4)(2x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^3+4x-2x^2-8)(2x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^4-x^3+2x^2-4x-24\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x^2+4\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x^2+4\right) = x^3+4x-2x^2-8 $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^3+4x-2x^2-8}\right) $ by each term in $ \left( 2x+3\right) $. $$ \left( \color{blue}{x^3+4x-2x^2-8}\right) \cdot \left( 2x+3\right) = 2x^4+3x^3+8x^2+12x-4x^3-6x^2-16x-24 $$ |
| ③ | Combine like terms: $$ 2x^4+ \color{blue}{3x^3} + \color{red}{8x^2} + \color{green}{12x} \color{blue}{-4x^3} \color{red}{-6x^2} \color{green}{-16x} -24 = 2x^4 \color{blue}{-x^3} + \color{red}{2x^2} \color{green}{-4x} -24 $$ |
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