$(1 + 3 x i) \cdot (3 - i) - (5 + 3 x i) \cdot (3 - i) = 4 i - 12$

Explanation

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$(1 + 3 x i) \cdot (3 - i) - (5 + 3 x i) \cdot (3 - i) \overset{◯}{1} 3 - i + 9 i x - 3 i^{2} x - (15 - 5 i + 9 i x - 3 i^{2} x) \overset{◯}{2} 3 - i + 9 i x - 3 i^{2} x - 15 + 5 i - 9 i x + 3 i^{2} x 3 - i + 9 i x - 3 i^{2} x - 15 + 5 i - 9 i x + 3 i^{2} x \overset{◯}{3} 4 i - 12$
①	Multiply each term of $(1 + 3 i x)$ by each term in $(3 - i)$ . $(1 + 3 i x) \cdot (3 - i) = 3 - i + 9 i x - 3 i^{2} x$ Multiply each term of $(5 + 3 i x)$ by each term in $(3 - i)$ . $(5 + 3 i x) \cdot (3 - i) = 15 - 5 i + 9 i x - 3 i^{2} x$
②	Remove the parentheses by changing the sign of each term within them. $- (15 - 5 i + 9 i x - 3 i^{2} x) = - 15 + 5 i - 9 i x + 3 i^{2} x$
③	Combine like terms: $3 - i + 9 i x - 3 i^{2} x - 15 + 5 i - 9 i x + 3 i^{2} x = 4 i - 12$

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(1+3xi)⋅(3−i)−(5+3xi)⋅(3−i)=4i−12

$(1 + 3 x i) \cdot (3 - i) - (5 + 3 x i) \cdot (3 - i) = 4 i - 12$