Discussion
In the expression \((5x - 3y)(6x + 5y) - (3x + 7y)(4x - 5y)\), what is the coefficient of xy?
Answer: A
The coefficient of xy is -6.
Only the cross terms of each product contain xy:
\[ \begin{aligned} (5x - 3y)(6x + 5y) &: 25xy - 18xy = 7xy \\ (3x + 7y)(4x - 5y) &: -15xy + 28xy = 13xy \\ 7xy - 13xy &= -6xy \end{aligned} \]
The second product is subtracted, so its xy term changes sign. Adding the two products instead would give 20, and the option 13 is the second product's coefficient on its own; forgetting the subtraction is the usual trap here.
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