因式分解：ab^2+bc^2+ca^2+a^2*b+b^2*c+c^2*a+2abc

ab^2+bc^2+ca^2+a^2*b+b^2*c+c^2*a+2abc
=(ab^2+c^2*a+2abc)+(bc^2+ca^2+a^2*b+b^2*c)
=a(b^2+c^2*+2bc)+(a^2*b+ca^2)+(bc^2+b^2*c)
=a(b+c)^2+a^2(b+c)+bc(b+c)
=(b+c)[a(b+c)+a^2+bc]
=(b+c)(ab+ac+a^2+bc)
=(b+c)[(ab+a^2)+(ac+bc)]
=(b+c)[a(a+b)+c(a+b)]
=(b+c)[(a+b)(a+c)]
=(b+c)(a+b)(a+c)