Question
Answer
$$4i\cdot(2-6i)\cdot(4+2i)=16i^2+80i+96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4i\cdot(2-6i)\cdot(4+2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(8i-24i^2)\cdot(4+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(8i+24)\cdot(4+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}32i+16i^2+96+48i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16i^2+80i+96\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4i} $ by $ \left( 2-6i\right) $ $$ \color{blue}{4i} \cdot \left( 2-6i\right) = 8i-24i^2 $$ |
| ② | $$ -24i^2 = -24 \cdot (-1) = 24 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{8i+24}\right) $ by each term in $ \left( 4+2i\right) $. $$ \left( \color{blue}{8i+24}\right) \cdot \left( 4+2i\right) = 32i+16i^2+96+48i $$ |
| ④ | Combine like terms: $$ \color{blue}{32i} +16i^2+96+ \color{blue}{48i} = 16i^2+ \color{blue}{80i} +96 $$ |
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