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