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