Question
Answer
$$(4(i+5))^2=160i+384$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4(i+5))^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4i+20)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}16i^2+160i+400 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-16+160i+400 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}160i+384\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( i+5\right) $ $$ \color{blue}{4} \cdot \left( i+5\right) = 4i+20 $$ |
| ② | Find $ \left(4i+20\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}{ 20 }$. $$ \begin{aligned}\left(4i+20\right)^2 = \color{blue}{\left( 4i \right)^2} +2 \cdot 4i \cdot 20 + \color{red}{20^2} = 16i^2+160i+400\end{aligned} $$ |
| ③ | $$ 16i^2 = 16 \cdot (-1) = -16 $$ |
| ④ | Combine like terms: $$ 160i \color{blue}{-16} + \color{blue}{400} = 160i+ \color{blue}{384} $$ |
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