Factorize completely \(x^{2} + 2xy + y^{2} + 3x + 3y – 18\).
-
(x+y+6)(x+y-3)
- (x-y-6)(x-y+3)
- (x-y+6)(x-y-3)
- (x+y-6)(x+y+3)
The correct answer is: A
Explanation
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: \(x^2 + xy + xy + y^2 +6x - 3x +6y - 3y - 18\)
= \(x^2 + 2xy + y^2 + 3x + 3y - 18\)