(b+c-a)(a-b-c)
=-(b+c-a)^2
=-(b+c)^2+2a(b+c)+a^2
=-b^2-2bc-c^2+2ab+2ac+a^2
a^4-(a-1)(a+1)(a^2+1)
=a^4-(a^2-1)(a^2+1)
=a^4-a^4+1
=1
(3x-2y+4z)(2y-3x+4z)
=-(2y-3x-4z)(2y-3x+4z)
=-(2y-3x)^2+16z^2
=-4y^2+12xy-9x^2+16z^2
(2a+b-3c)^2
=(2a+b)^2-6c(2a+b)+9c^2
=4a^2+4ab+b^2-12ac-6bc+9c^2