Let P = 12xy − 10y² − 18x², Q = 14x² + 12y² + 9xy, and R = 5y² − x² + xy then (P + Q) − R =

P + Q = (12xy + 9xy) + (−10y² + 12y²) + (−18x² + 14x²) = 21xy + 2y² − 4x². Then (P + Q) − R = 21xy + 2y² − 4x² − (5y² − x² + xy) = 21xy − xy + 2y² − 5y² − 4x² + x² = 20xy − 3y² − 3x². Hmm, this gives 20xy − 3x² − 3y², matching option (4). Let me recheck: 21xy − xy = 20xy; 2y² − 5y² = −3y²; −4x² + x² = −3x². So result is 20xy − 3x² − 3y², which is option (4).