因式分解（1）x^2+2xy-x-y+y^2-2 (2) x^2-2xy+3x-3y+y^2+2

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因式分解（1）x^2+2xy-x-y+y^2-2 (2) x^2-2xy+3x-3y+y^2+2
因式分解（1）x^2+2xy-x-y+y^2-2 (2) x^2-2xy+3x-3y+y^2+2

因式分解（1）x^2+2xy-x-y+y^2-2 (2) x^2-2xy+3x-3y+y^2+2
1.x^2+2xy-x-y+y^2-2
=x^2-1+y^2-1+xy-x+xy-y
=(x+1)(x-1)+(y+1)(y-1)+x(y-1)+y(x-1)
=(x+y+1)(x-1)+(x+y+1)(y-1)=(x+y+1)(x+y-2)
2.x^2-2xy+3x-3y+y^2+2
=x^2-1+y^2-1+x-xy-y-xy+2x+2-2y+2
=(x+1)(x-1)+(y+1)(y-1)-x(y-1)-y(x+1)+2(x+1)-2(y-1)
=(x+1)(x-y+1)+(y-x-1)(y-1)=(x-y+1)(x-y+2)

（1）x^2+2xy-x-y+y^2-2
=x²+2xy+y²-x-y-2
=(x+y)²-(x+y)-2
=(x+y-2)(x+y+1)
(2) x^2-2xy+3x-3y+y^2+2
=x²-2xy+y²+3x-3y+2
=(x-y)²+3(x-y)+2
=(x-y+2)(x-y+1)

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

(1)(x+y-2)(x+y+1)
(2)(x-y+1)(x-y+2)

x^2+2xy+y^2-3x-3y+2
=(x+y)²-3(x+y)+2
=(x+y-1)(x+y-2)
十字相乘法
(x+y) -1
(x+y) -2

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