(xy+1)^2+(x+y)(x+y-2xy-2)怎么解啊是因式分解
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/08/05 11:28:05
(xy+1)^2+(x+y)(x+y-2xy-2)怎么解啊是因式分解
![(xy+1)^2+(x+y)(x+y-2xy-2)怎么解啊是因式分解](/uploads/image/z/19156669-61-9.jpg?t=%28xy%2B1%29%5E2%2B%28x%2By%29%28x%2By-2xy-2%29%E6%80%8E%E4%B9%88%E8%A7%A3%E5%95%8A%E6%98%AF%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3)
令a=xy,b=x+y
原式=(a+1)²+b(b-2a-2)
=a²+2a+1+b²-2ab-2b
=(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
=(y-1)²(x-1)²
原式=(a+1)²+b(b-2a-2)
=a²+2a+1+b²-2ab-2b
=(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
=(y-1)²(x-1)²