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