(1+x)²(1+y²)-(1+x²)(1+y)²
=[(1+x²)+2x][(1+y)²-2y]-(1+x²)(1+y)²
=(1+x²)(1+y)²-2y(1+x²)+2x(1+y)²-4xy-(1+x²)(1+y)²
=-2y(1+x²)+2x(1+y)²-4xy
=﹣2y-2x²y+2x(1+2y+y²)-4xy
=﹣2y-2x²y+2x+4xy+2xy²-4xy
=(2x-2y)-(2x²y-2xy²)
=2(x-y)-2xy(x-y)
=2(x-y)(1-xy)
不懂的还可以追问!满意请及时采纳! O(∩_∩)O
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