(a+b-c-d)(a-b+c+d)
=[a+(b-c-d)][a-(b-c-d)]
=a²-(b-c-d)²
=a²-(b-c-d)(b-c-d)
=a²-[b(b-c-d)-c(b-c-d)-d(b-c-d)]
=a²-(b²-bc-bd-bc+c²+cd-bd+cd+d²)
=a²-(b²+c²+d²-2bc-2bd+2cd)
=a²-b²-c²-d²+2bc+2bd-2cd
(a+b-c-d)(a-b+c+d)
=[a+(b-c-d)][a-(b-c-d)]
=a²-(b-c-d)²
=a²-(b-c-d)(b-c-d)
=a²-[b(b-c-d)-c(b-c-d)-d(b-c-d)]
=a²-(b²-bc-bd-bc+c²+cd-bd+cd+d²)
=a²-(b²+c²+d²-2bc-2bd+2cd)
=a²-b²-c²-d²+2bc+2bd-2cd