Discussion
Let
\(P = 12xy - 10y^{2} - 18x^{2}\),
\(Q = 14x^{2} + 12y^{2} + 9xy\), and
\(R = 5y^{2} - x^{2} + xy\)
then \((P + Q) - R =\)
Answer: D
\((P + Q) - R\) equals \(20xy - 3x^{2} - 3y^{2}\).
Collect like terms in \(P + Q\), then subtract each term of R.
\[ \begin{aligned} P + Q &= 21xy + 2y^{2} - 4x^{2} \\ -R &= -5y^{2} + x^{2} - xy \\ \text{total} &= 20xy - 3x^{2} - 3y^{2} \end{aligned} \]
The xy terms give \(12 + 9 - 1 = 20\), the \(x^{2}\) terms give \(-18 + 14 + 1 = -3\), and the \(y^{2}\) terms give \(-10 + 12 - 5 = -3\).
Options starting with \(22xy\) add the xy term of R instead of subtracting it, and \(-7x^{2}\) does not come from any correct grouping of the \(x^{2}\) terms.
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