factorization

x^2+4x+4
x^2+2(2x)(2)+2^2
(x+2)^2
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y^2-6y+9
y^2-2(y)(3)+3^2
(y-3)^2
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x^2-y^2+4x+6y-5
(x^2+4x+4)-(y^2-6y+9)
(x+2)^2-(y-3)^2
(x+2-y+3)(x+2+y-3)
(x-y+5)(x+y-1)

2010-10-28 17:54:26 補充：
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2010-10-28 17:56:05 補充：
More detail:
x^2-y^2+4x+6y-5
x^2-y^2+4x+6y+4-9
(x^2+4x+4)-(y^2-6y+9)
(x+2)^2-(y-3)^2
(x+2-y+3)(x+2+y-3)
(x-y+5)(x+y-1)

x^2+4x+4
= (x+2)^2

y-6y+9
係咪應該y^2-6y+9 ??
y^2-6y+9
=(y-3)^2

hence ,
x^2-y^2+4x+6y-5
=(x^2+4x+4) - (y^2-6y+9)
=(x+2)^2 - (y-3)^2
=[(x+2)+(y-3)] [(x+2)-(y-3)]
= (x+2+y-3) (x+2-y+3)
= (x+y-1) (x-y+5)