1-xy(1-xy)-x^3y^3
=(1-xy)(1+xy+x^2y^2)-xy(1-xy)
=(1-xy)(1+xy)^2
ab(c+d)(c-d)+cd(a+b)(a-b)
=ac(bc+ad)-bd(bc+ad)
=(ad-bd)(bc+ad)
1-xy(1-xy)-x^3y^3
=(1-xy)(1+xy+x^2y^2)-xy(1-xy)
=(1-xy)(1+xy)^2
ab(c+d)(c-d)+cd(a+b)(a-b)
=ac(bc+ad)-bd(bc+ad)
=(ad-bd)(bc+ad)