Question
Answer
$$(-8i)\cdot(8-i)\cdot(6+3i)=-192i^2-408i-48$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-8i)\cdot(8-i)\cdot(6+3i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-64i+8i^2)\cdot(6+3i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-64i-8)\cdot(6+3i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-384i-192i^2-48-24i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-192i^2-408i-48\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{-8i} $ by $ \left( 8-i\right) $ $$ \color{blue}{-8i} \cdot \left( 8-i\right) = -64i+8i^2 $$ |
| ② | $$ 8i^2 = 8 \cdot (-1) = -8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{-64i-8}\right) $ by each term in $ \left( 6+3i\right) $. $$ \left( \color{blue}{-64i-8}\right) \cdot \left( 6+3i\right) = -384i-192i^2-48-24i $$ |
| ④ | Combine like terms: $$ \color{blue}{-384i} -192i^2-48 \color{blue}{-24i} = -192i^2 \color{blue}{-408i} -48 $$ |
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