Discussion
If \(5x^{2} - 8y - 20x + 2xy = (x + a)(bx + 2y)\), then the value of (a - b) is :
Answer: C
The value of (a - b) is -9.
Expand the right-hand side and compare coefficients:
\[ \begin{aligned} (x + a)(bx + 2y) &= bx^{2} + 2xy + abx + 2ay \\ b &= 5,\quad 2a = -8 \Rightarrow a = -4 \\ ab &= -20\ \text{(checks with } -20x) \\ a - b &= -4 - 5 = -9 \end{aligned} \]
9 is b - a, the subtraction done the wrong way round, and -1 and 1 come from taking a = 4 or mixing up the signs.
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