（1）x^2+y^2-4x+2y+5=0,则x+2y= （2）-3x^2+6xy-3y^2

x^3-3x^2+6xy-12y^2+8y^3
=(x+2y)(x^2-2xy+4y^2)-3(x^2-2xy+4y^2)
=(x^2-2xy+4y^2)(x+2y-3)
x^2-2xy+y^2-2x+2y+1
=(x-y)^2-2(x-y)+1=(x-y-1)^2
a^2(a+1)-b^2(b+1)=a^3-b^3+(a^2-b^2)
=(a-b)(a^2+ab+b^2+a+b)
(a-4)^2+(b-4)^2+2(ab-8)
=a^2+b^2+2ab-8(a+b)+16
=(a+b-4)^2
(x^2+x+1)(x^2+x+2)-6
=(x^2+x+1)^2+(x^2+x+1)-6
=(x^2+x+4)(x^2+x-1)
当x-y=1时,
x^4-xy^3-x^3y-3x^2y+3xy^2+y^4
=(x^4+y^4-2x^2y^2)-(xy^3+x^3y-2x^2y^2)-3xy(x-y)
=(x+y)^2-xy-3xy
=(x-y)^2
=1

2x^2+4xy-2x-y+2=0 6x^2+12xy-6x-3y+6=0
3x^2+6xy-x+4y=0 6x^2+12xy-2x-8y=0
-4x+5y+6=0 5y=4x-6 y=(4x-6)/5
3x^2+6x(4x-6)/5-x+4(4x-6)/5=0
15x^2+6x(4x-6)-5x+4(4x-6)=0
15x^2+24x^2-36x-5x+16x-24=0
39x^2-25x-24=0
x^2-25x/39=24/39
x^2-25x/39+(25/78)^2=24/39+625/6084
(x-25/78)^2=3744/6084+625/6084
x-25/78=±√(4369/6084)
x=25/78±√4369/78
x=(25±√4369)/78
y=[4(25±√4369)/78-6]/5
=[2(25±√4369)/39-6]/5
=[(50±2√4369)/78-6]/5
=[(50±2√4369-468)/78]/5
=[(±2√4369-418)/78]/5
=(±2√4369-418)/390

1.x+y
2.2(a-b)(a+b)

(1)3x^2+6xy =3x(x+2y)
(2)2x(x-y)+x^2(y-x)=x(x-y)(2-x)
(3)题目是否有问题,应该为：x^3y-2x^2y^2+xy^3,如果是,解答如下
x^3y-2x^2y^2+xy^3=xy(x^2-2xy+y^2)=xy(x-y)^2
(4)4a^2+16b^2+8ab=4(a^2+4ab+4b^2)=4(a+2b)^2

-3x^2+6xy-3x
=-3x(x-2y+1)

-3x^2+6xy-3y^2 =-3（x^2-2xy+y^2） =-3（x-y）^2

x=-1 y=-1或-1/2