数学因式分解，要详解

1、（ab+1)(a+1)(b+1)+ab
=（ab+1)(ab+1+a+b)+ab
=(ab+1)²+(a+b)(ab+1)+ab
（把ab+1看做一项）
=（ab+a+1)(ab+b+1)

2、x^4-(a+b)x^3+(a^2b+ab^2)x-a^2b^2
=(x^4-a²b²)-[(a+b)x³-ab(a+b)x]
=(x²-ab)(x²+ab)-(a+b)x(x²-ab)
=(x²-ab)[x²-(a+b)x+ab]
=(x²-ab)(x-a)(x-b)

3、(xy-1)^2+(x+y-2)(x+y-2xy)
设xy=a,x+y=b
原式
=(a-1)²+(b-2)(b-2a)
=a²-2a+1+b²-2b-2ab+4a
=a²-2ab+b²+2a-2b+1
=(a-b)²-2(a-b)+1
=(a-b+1)²
=(xy-x-y+1)²
[x(y-1)-(y-1)]²
=(x-1)²(y-1)²