Question
Answer
$$3i\cdot(2-5i)\cdot(2+3i)=18i^2+57i+30$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3i\cdot(2-5i)\cdot(2+3i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6i-15i^2)\cdot(2+3i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6i+15)\cdot(2+3i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}12i+18i^2+30+45i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}18i^2+57i+30\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3i} $ by $ \left( 2-5i\right) $ $$ \color{blue}{3i} \cdot \left( 2-5i\right) = 6i-15i^2 $$ |
| ② | $$ -15i^2 = -15 \cdot (-1) = 15 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{6i+15}\right) $ by each term in $ \left( 2+3i\right) $. $$ \left( \color{blue}{6i+15}\right) \cdot \left( 2+3i\right) = 12i+18i^2+30+45i $$ |
| ④ | Combine like terms: $$ \color{blue}{12i} +18i^2+30+ \color{blue}{45i} = 18i^2+ \color{blue}{57i} +30 $$ |
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