Question
Answer
$$0.09(z-1)^2=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}0.09(z-1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}0.09(1z^2-2z+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0z^2+0z+0 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}0\end{aligned} $$ | |
| ① | Find $ \left(z-1\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ z } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(z-1\right)^2 = \color{blue}{z^2} -2 \cdot z \cdot 1 + \color{red}{1^2} = z^2-2z+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{0} $ by $ \left( z^2-2z+1\right) $ $$ \color{blue}{0} \cdot \left( z^2-2z+1\right) = 0z^20z0 $$ |
| ③ | Combine like terms: $$ 0 = 0 $$ |
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