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
\(x^{2} + 2xy + y^{2} + 3x + 3y - 18\)
\(x^{2} + 2xy + 3x + y^{2} + 3y -18\)
\(x^{2} + 2xy - 3x + 6x + y^{2} -3y + 6y -18\)
\(x^{2} + 2xy -3x + y^{2} -3y + 6x + 6y -18\)
\(x^{2} + xy -3x + xy + y^{2} - 3y + 6x + 6y -18\)
x(x + y - 3) + y(x + y - 3) + 6(x + y - 3)
= (x + y - 3)(x + y + 6)
= (x + y + 6)(x + y -3)
Source: Myschool Past Questions Archive (Record #46359)