Question

分解因式(x+y)(x+y+2xy)+(xy+1)(xy-1)

Answer 1

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

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

=(x+y+xy+1)(x+y+xy-1) (十字相乘法分解)

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

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

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