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

* Hướng dẫn giải

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

$={\left[\left(a+b\right)+\left(c+d\right)\right]}^2+{\left[\left(a+b\right)-\left(c+d\right)\right]}^2+{\left[\left(a+c\right)-\left(b+d\right)\right]}^2+{\left[\left(a+d\right)\left(b+c\right)\right]}^2$

$=2{\left(a+b\right)}^2+2{\left(c+d\right)}^2+{\left(a+c\right)}^2+{\left(b+d\right)}^2+{\left(a+d\right)}^2+{\left(b+c\right)}^2-2\left(ad+bc+ac+bd\right)$

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