Question
Answer
$$(2+i)\cdot(9+3i)\cdot(-8-8i)=-120i^2-240i-120$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2+i)\cdot(9+3i)\cdot(-8-8i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(18+6i+9i+3i^2)\cdot(-8-8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(3i^2+15i+18)\cdot(-8-8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(-3+15i+18)\cdot(-8-8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(15i+15)\cdot(-8-8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-120i-120i^2-120-120i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-120i^2-240i-120\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2+i}\right) $ by each term in $ \left( 9+3i\right) $. $$ \left( \color{blue}{2+i}\right) \cdot \left( 9+3i\right) = 18+6i+9i+3i^2 $$ |
| ② | Combine like terms: $$ 18+ \color{blue}{6i} + \color{blue}{9i} +3i^2 = 3i^2+ \color{blue}{15i} +18 $$ |
| ③ | $$ 3i^2 = 3 \cdot (-1) = -3 $$ |
| ④ | Combine like terms: $$ \color{blue}{-3} +15i+ \color{blue}{18} = 15i+ \color{blue}{15} $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{15i+15}\right) $ by each term in $ \left( -8-8i\right) $. $$ \left( \color{blue}{15i+15}\right) \cdot \left( -8-8i\right) = -120i-120i^2-120-120i $$ |
| ⑥ | Combine like terms: $$ \color{blue}{-120i} -120i^2-120 \color{blue}{-120i} = -120i^2 \color{blue}{-240i} -120 $$ |
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