Question

因式分解：（1-x²）（1-y²）+4xy

因式分解：（1-x²）（1-y²）+4xy

Answer 1

解辩改由（1-x²段告）握灶明（1-y²）+4xy

=x^2y^2-x^2-y^2+1+4xy
=x^2y^2+2xy+1-(x^2-2xy+y^2)
=(xy+1)^2-(x-y)^2
=[(xy+1)+(x-y)][(xy+1)-(x-y)]
=(xy+x-y+1)(xy-x+y+1)

Answer 2

1-y²-x²+x²y²+4XY
=1-X²咐散腔态Y²+2XY-(X²衡圆氏-2XY+Y²)
=1-XY(XY+2)-(X-Y)²
=(1+X-Y)(1-X+Y)-XY(XY+2)

Answer 3

（1-x²山老搭）（含简1-y²）逗拿+4xy
=x²y²+2xy+1-x²-y²+2xy
=(xy+1)^2-(x-y)^2

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