Question
Answer
$$(4i+6)^2=48i+20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4i+6)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16i^2+48i+36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-16+48i+36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}48i+20\end{aligned} $$ | |
| ① | Find $ \left(4i+6\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 4i } $ and $ B = \color{red}{ 6 }$. $$ \begin{aligned}\left(4i+6\right)^2 = \color{blue}{\left( 4i \right)^2} +2 \cdot 4i \cdot 6 + \color{red}{6^2} = 16i^2+48i+36\end{aligned} $$ |
| ② | $$ 16i^2 = 16 \cdot (-1) = -16 $$ |
| ③ | Combine like terms: $$ 48i \color{blue}{-16} + \color{blue}{36} = 48i+ \color{blue}{20} $$ |
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