x^2+3x-y-2xy-3y^2+2(要详细过程)

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x^2+3x-y-2xy-3y^2+2(要详细过程)x^2+3x-y-2xy-3y^2+2(要详细过程)x^2+3x-y-2xy-3y^2+2(要详细过程)x²+3x-y-2xy-3y

x^2+3x-y-2xy-3y^2+2(要详细过程)
x^2+3x-y-2xy-3y^2+2(要详细过程)

x^2+3x-y-2xy-3y^2+2(要详细过程)
x²+3x-y-2xy-3y²+2
=(x²-2xy-3y²)+(3x-y)+2
=(x-3y)(x+y)+(3x-y)+2
=(x-3y)(x+y)+[(x-3y)+2(x+y)]+1×2 (十字相乘法)
=(x-3y+2)(x+y+1)
如不明白十字相乘法,可看下面直接提取公因式:
x²+3x-y-2xy-3y²+2
=(x²-2xy-3y²)+(3x-y)+2
=(x-3y)(x+y)+(3x-y)+2
=(x-3y)(x+y)+(x-3y)+2(x+y)+2
=(x-3y)(x+y+1)+2(x+y+1)
=(x-3y+2)(x+y+1)