$(1 + i s q r t \cdot 3)^{2} = 9 i^{2} q^{2} r^{2} s^{2} t^{2} + 6 i q rs t + 1$

Explanation

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$(1 + i s q r t \cdot 3)^{2} \overset{◯}{1} 1 + 6 i q rs t + 9 i^{2} q^{2} r^{2} s^{2} t^{2} \overset{◯}{2} 9 i^{2} q^{2} r^{2} s^{2} t^{2} + 6 i q rs t + 1$
①	Find $(1 + 3 i q rs t)^{2}$ using formula. $(A + B)^{2} = A^{2} + 2 \cdot A \cdot B + B^{2}$ where $A = 1$ and $B = 3 i q rs t$ . $(1 + 3 i q rs t)^{2} = 1^{2} + 2 \cdot 1 \cdot 3 i q rs t + (3 i q rs t)^{2} = 1 + 6 i q rs t + 9 i^{2} q^{2} r^{2} s^{2} t^{2}$
②	Combine like terms: $9 i^{2} q^{2} r^{2} s^{2} t^{2} + 6 i q rs t + 1 = 9 i^{2} q^{2} r^{2} s^{2} t^{2} + 6 i q rs t + 1$

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(1+isqrt⋅3)2=9i2q2r2s2t2+6iqrst+1

$(1 + i s q r t \cdot 3)^{2} = 9 i^{2} q^{2} r^{2} s^{2} t^{2} + 6 i q rs t + 1$