Answer
$$(1+isqrt\cdot3)^2=9i^2q^2r^2s^2t^2+6iqrst+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+isqrt\cdot3)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1+6iqrst+9i^2q^2r^2s^2t^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9i^2q^2r^2s^2t^2+6iqrst+1\end{aligned} $$ | |
| ① | Find $ \left(1+3iqrst\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 1 } $ and $ B = \color{red}{ 3iqrst }$. $$ \begin{aligned}\left(1+3iqrst\right)^2 = \color{blue}{1^2} +2 \cdot 1 \cdot 3iqrst + \color{red}{\left( 3iqrst \right)^2} = 1+6iqrst+9i^2q^2r^2s^2t^2\end{aligned} $$ |
| ② | Combine like terms: $$ 9i^2q^2r^2s^2t^2+6iqrst+1 = 9i^2q^2r^2s^2t^2+6iqrst+1 $$ |
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