Question

分解因式：(X+Y）*（X+Y+2XY）+（XY+1）*（XY-1）

Answer 1

原式=(x+y)(x+y)+2(x+y)xy+(xy)^2-1^2

=(x+y)^2+2(x+y)xy+(xy)^2-1

=(x+y+xy)^2-1

=(x+y+xy-1)(x+y+xy+1)

=(x+y+xy-1)(x+1)(y+1)