Factorize completely X2+2XY+Y2+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)
Correct Answer: Option A
Explanation
(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)
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