Question
Answer
$$(-6i)\cdot(-5-4i)\cdot(4+4i)=120i^2+24i-96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-6i)\cdot(-5-4i)\cdot(4+4i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(30i+24i^2)\cdot(4+4i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(30i-24)\cdot(4+4i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}120i+120i^2-96-96i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}120i^2+24i-96\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{-6i} $ by $ \left( -5-4i\right) $ $$ \color{blue}{-6i} \cdot \left( -5-4i\right) = 30i+24i^2 $$ |
| ② | $$ 24i^2 = 24 \cdot (-1) = -24 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{30i-24}\right) $ by each term in $ \left( 4+4i\right) $. $$ \left( \color{blue}{30i-24}\right) \cdot \left( 4+4i\right) = 120i+120i^2-96-96i $$ |
| ④ | Combine like terms: $$ \color{blue}{120i} +120i^2-96 \color{blue}{-96i} = 120i^2+ \color{blue}{24i} -96 $$ |
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