Concept:Recognize the first three terms as a perfect square and then factor the quadratic in x+y.Explanation:Group the expression: x2+2xy+y2+3x+3y−18=(x2+2xy+y2)+3(x+y)−18.Since x2+2xy+y2=(x+y)2, the expression becomes (x+y)2+3(x+y)−18.Let t=x+y. Then t2+3t−18=(t+6)(t−3).Substitute back: (x+y+6)(x+y−3).Answer:(x+y+6)(x+y−3), which is option A.