Answer
$$(z-4)(z^2-8z+52)=z^3-12z^2+84z-208$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(z-4)(z^2-8z+52)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}z^3-8z^2+52z-4z^2+32z-208 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}z^3-12z^2+84z-208\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{z-4}\right) $ by each term in $ \left( z^2-8z+52\right) $. $$ \left( \color{blue}{z-4}\right) \cdot \left( z^2-8z+52\right) = z^3-8z^2+52z-4z^2+32z-208 $$ |
| ② | Combine like terms: $$ z^3 \color{blue}{-8z^2} + \color{red}{52z} \color{blue}{-4z^2} + \color{red}{32z} -208 = z^3 \color{blue}{-12z^2} + \color{red}{84z} -208 $$ |
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