Question
Answer
$$-2(-4i-3)(-4i-3)-(5i-3)+10i=-43i+17$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-2(-4i-3)(-4i-3)-(5i-3)+10i& \xlongequal{ }-(-8i-6)(-4i-3)-(5i-3)+10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(32i^2+24i+24i+18)-(5i-3)+10i \xlongequal{ } \\[1 em] & \xlongequal{ }-(32i^2+48i+18)-(5i-3)+10i \xlongequal{ } \\[1 em] & \xlongequal{ }-(-32+48i+18)-(5i-3)+10i \xlongequal{ } \\[1 em] & \xlongequal{ }-(48i-14)-(5i-3)+10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-48i+14-(5i-3)+10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-48i+14-5i+3+10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-43i+17\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-8i-6}\right) $ by each term in $ \left( -4i-3\right) $. $$ \left( \color{blue}{-8i-6}\right) \cdot \left( -4i-3\right) = 32i^2+24i+24i+18 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left(48i-14 \right) = -48i+14 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5i-3 \right) = -5i+3 $$ |
| ④ | Combine like terms: $$ \color{blue}{-48i} + \color{red}{14} \color{green}{-5i} + \color{red}{3} + \color{green}{10i} = \color{green}{-43i} + \color{red}{17} $$ |
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