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