Answer
$$(-4x-4i\cdot3)^3=-1728i^2x-576ix^2-64x^3+1728i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-4x-4i\cdot3)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-4x-12i)^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-64x^3-576ix^2-1728i^2x-1728i^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-64x^3-576ix^2-1728i^2x--1728i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-1728i^2x-576ix^2-64x^3+1728i\end{aligned} $$ | |
| ① | $$ 4 i \cdot 3 = 12 i $$ |
| ② | Find $ \left(-4x-12i\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = -4x $ and $ B = 12i $. $$ \left(-4x-12i\right)^3 = \left( -4x \right)^3-3 \cdot \left( -4x \right)^2 \cdot 12i + 3 \cdot \left( -4x \right) \cdot \left( 12i \right)^2-\left( 12i \right)^3 = -64x^3-576ix^2-1728i^2x-1728i^3 $$ |
| ③ | $$ 1728i^3 = 1728 \cdot \color{blue}{i^2} \cdot i =
1728 \cdot ( \color{blue}{-1}) \cdot i =
-1728 \cdot \, i $$ |
| ④ | Combine like terms: $$ -1728i^2x-576ix^2-64x^3+1728i = -1728i^2x-576ix^2-64x^3+1728i $$ |
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