$(4 + 3 y i) \cdot (3 + 4 i) - (4 + 5 y i) \cdot (3 + 4 i) = - 8 i^{2} y - 6 i y$

Explanation

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$(4 + 3 y i) \cdot (3 + 4 i) - (4 + 5 y i) \cdot (3 + 4 i) \overset{◯}{1} 12 + 16 i + 9 i y + 12 i^{2} y - (12 + 16 i + 15 i y + 20 i^{2} y) \overset{◯}{2} 12 + 16 i + 9 i y + 12 i^{2} y - 12 - 16 i - 15 i y - 20 i^{2} y 12 + 16 i + 9 i y + 12 i^{2} y - 12 - 16 i - 15 i y - 20 i^{2} y \overset{◯}{3} - 8 i^{2} y - 6 i y$
①	Multiply each term of $(4 + 3 i y)$ by each term in $(3 + 4 i)$ . $(4 + 3 i y) \cdot (3 + 4 i) = 12 + 16 i + 9 i y + 12 i^{2} y$ Multiply each term of $(4 + 5 i y)$ by each term in $(3 + 4 i)$ . $(4 + 5 i y) \cdot (3 + 4 i) = 12 + 16 i + 15 i y + 20 i^{2} y$
②	Remove the parentheses by changing the sign of each term within them. $- (12 + 16 i + 15 i y + 20 i^{2} y) = - 12 - 16 i - 15 i y - 20 i^{2} y$
③	Combine like terms: $12 + 16 i + 9 i y + 12 i^{2} y - 12 - 16 i - 15 i y - 20 i^{2} y = - 8 i^{2} y - 6 i y$

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(4+3yi)⋅(3+4i)−(4+5yi)⋅(3+4i)=−8i2y−6iy

$(4 + 3 y i) \cdot (3 + 4 i) - (4 + 5 y i) \cdot (3 + 4 i) = - 8 i^{2} y - 6 i y$