Question

因式分解a^3+b^3+c^3-a*(b-c)^2-b*(c-a)^2-c*(a-b)^2-4*a*b*c

a^3+b^3+c^3-a*(b-c)^2-b*(c-a)^2-c*(a-b)^2-4*a*b*c

Answer 1

a^3+b^3+c^3-a*(b-c)^2-b*(c-a)^2-c*(a-b)^2-4*a*b*c

=a³+b³+c³-a(b²+c²-2bc)-b(a²+c²-2ac)-c(a²+b²-2ab)-4abc
=a³+b³+c³-ab²-ac²+2abc-a²b+bc²+2abc-a²c-b²c+2abc-4abc
=a³+b³+c³-ab²-b²c-ac²-bc²-a²b-a²c+2abc
=a³+b³+c³-b²(a+c)-c²(a+b)-a²(b+c)+2abc
=-(b+c-a)(c+a-b)(a+b-c)