Discussion
If \(A = x^{2}(1 - 3y^{2})\), \(B = x(xy^{2} - 2x)\) and \(C = 3y(y - 4x^{2}y)\), then \(A + B - C = px^{2} + qx^{2}y^{2} + ry^{2}\).
What is the value of (5p + q - r) ?
Answer: D
The value of (5p + q - r) is 8.
\[ \begin{aligned} A &= x^{2} - 3x^{2}y^{2} \\ B &= x^{2}y^{2} - 2x^{2} \\ C &= 3y^{2} - 12x^{2}y^{2} \\ A + B - C &= -x^{2} + 10x^{2}y^{2} - 3y^{2} \end{aligned} \]
So p = -1, q = 10, r = -3, and 5p + q - r = -5 + 10 + 3 = 8.
10 is q alone. 12 and 18 come from sign slips; the step that most often goes wrong is subtracting C, which turns its -12x²y² into +12x²y² and its 3y² into -3y².
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