Xét tổng: \(ab+2ac-abc+bc-a^2c-ac^2+a^2+c^2\)ta có:
\(ab+2ac-abc+bc-a^2c-ac^2+a^2+c^2\)
\(=\left(a^2+2ac+c^2\right)+\left(ab+bc\right)-\left(abc+a^2c+ac^2\right)\)
\(=\left(a+c\right)^2+b\left(a+c\right)-ac\left(a+b+c\right)\)
\(=\left(a+c\right)\left(a+c+b\right)-ac\left(a+b+c\right)\)
mà \(a+b+c=0\)( giả thiết )
\(\Rightarrow ab+2ac-abc+bc-a^2c-ac^2+a^2+c^2=0\)
hay \(ab+2ac-abc+bc-a^2c-ac^2=-a^2-c^2\)( đpcm )