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