Question

a2(b+c)2+b2(c+a)2+c2(a+b)2+abc(a+b+c)+(a2+b2+c2)(ab+bc+ca)因式

Answer 1

设u=a+b+c,v=ab+bc+ca,w=abc,有恒等式a^2+b^2+c^2=u^2-2v,a^2b^2+b^2c^2+c^2a^2=v^2-2uw,a^2(b+c)^2+b^2(c+a)^2+c^2(a+b)^2=2(v^2-2uw)+2uw=2v^2-2uw,(a+b)(b+c)(c+a)=uv-w,∴原式=2v^2-2uw+uw+(u^2-2v)v=u^2v-uw=u(...