Factorize completely \(x^{2} + 2xy + y^{2} + 3x + 3y - 18\).
A
(x+y+6)(x+y-3)
B
(x-y-6)(x-y+3)
C
(x-y+6)(x-y-3)
D
(x+y-6)(x+y+3)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Expand the options and collect like terms to check which gives the presented expression.
Expansion of Options A:
(x+y+6)(x+y-3) → \(x^2+xy-3x + xy+y^2-3y +6x+6y-18\)
Collect like terms: \(x^2 + xy + xy + y^2 +6x - 3x +6y - 3y - 18\)
= \(x^2 + 2xy + y^2 + 3x + 3y - 18\)
Source: Myschool Past Questions Archive (Record #20)