因式分解：（x+y-2xy)(x+y-2)+(1+xy)2 (a2+9b2-1)2-36a2b2 2x2-7xy-22y2-5x=35y-3 x2+3xy+2y2+4x+5y+3

题目

因式分解：（x+y-2xy)(x+y-2)+(1+xy)2 (a2+9b2-1)2-36a2b2 2x2-7xy-22y2-5x=35y-3 x2+3xy+2y2+4x+5y+3
x9+x6+x3-3

答案

（x+y-2xy)(x+y-2)+(1+xy)2
=(x+y)²-2(x+y)(xy+1)+4xy+(1+xy)² 怀疑后面是(1-xy)²
题目可能有问题
(a2+9b2-1)2-36a2b2
=(a²+9b²-1+6ab)(a²+9b²-1-6ab)
=[(a+3b)²-1][(a-3b)²-1]
=(a+3b+1)(a+3b-1)(a-3b+1)(a-3b-1)
2x2-7xy-22y2-5x+35y-3
=(2x-11y)(x+2y)-5x+35y-3
=(2x-11y+1)(x+2y-3)
x2+3xy+2y2+4x+5y+3
=(x+y)(x+2y)+4x+5y+3
=(x+y+1)(x+2y+3)
x9+x6+x3-3
=x^9-1+x^6-1+x³-1
=(x³-1)(x^6+x³+1)+(x³-1)(x³+1)+(x³-1)
=(x³-1)(x^6+2x³+2)
=(x-1)(x²+x+1)(x^6+2x³+2)