Question

因式分解：1、x^2y^2-x^2-y^2+1= 2、6x^2-5xy-6y^2+2x+

因式分解：1、x^2y^2-x^2-y^2+1= 2、6x^2-5xy-6y^2+2x+ 23y-20=
3、（x^4-4x^2+1)(x^4+3x^2+1)+10x^4=

Answer 1

x^2y^2-x^2-y^2+1
=(x^2y^2-2xy+1)-(x^2-2xy+y^2)
=(xy-1)^2-(x-y)^2
=(xy-x+y-1)(xy+x-y-1)
6x^2+2x-5xy-6y^2+23y-20
=6x^2-5xy-6y^2+2x+23y-20
=(3x+2y)(2x-3y)+2x+23y-20
=(3x+2y-5)(2x-3y+4)
原式=[(x^4+1)-4x²][(x^4+1)+3x²]+10x^4
=(x^4+1)²-x²(x^4+1)-12x^4+10x^4
=(x^4+1)²-x²(x^4+1)-2x^4
=(x^4+1-2x²)(x^4+1+x²)
=(x²-1)²[(x^4+2x²+1)-x²]
=(x+1)²(x-1)²[(x²+1)²-x²]
=(x+1)²(x-1)²(x²+x+1)(x²-x+1)

Answer 2

1、x²y²-x²-y²+1=(x²y²-x²)-(y²-1)=x²(y²-1)-(y²-1)=(x²-1)(y²-1)