Rút gọn biểu thức: (a+b+c)^2 +(a-b-c)^2 +(b-c-a)^2 +(c-a-b)^2

* Hướng dẫn giải

${\left(a+b+c\right)}^2+{\left(a-b-c\right)}^2+{\left(b-c-a\right)}^2+{\left(c-a-b\right)}^2$

$=\left(a^2+b^2+c^2+2ab+2ac+2bc\right)+\left(a^2+b^2+c^2-2ab-2ac+2bc\right)+\left(a^2+b^2+c^2-2ab+2ac-2bc\right)$

$=4\left(a^2+b^2+c^2\right)$