# Let a,b,c be real numbers such that a^3+b^3+c^3=1. Find that value of a(ab+c^2)+b(bc+a^2)+c(ca+b^a).

8 years ago
$(a+b+c)^{3}=$

$(a+b+c)^{3}-a^{3}-b^{3}-c^{3}-6abc=3a(ab+c^{2})+3b(bc+a^{2})+3c(ca+b^{2})$

$\frac{(a+b+c)^{3}-a^{3}-b^{3}-c^{3}-6abc}{3}=a(ab+c^{2})+b(bc+a^{2})+c(ca+b^{2})$