Đáp án:
$4a^2+4b^2+4c^2+4ab-4bc$
Giải thích các bước giải:
$( a + b + c ) ^2 + (a- b + c )^2 + ( a+b - c)^2 + ( b -c +a)^2$
$=(a^2+b^2+c^2+2ab+2bc+2ac)+(a^2−2ab+b^2−2bc+2ac+c^2)+(a^2+2ab+b^2−2bc−2ac+c^2)+(b^2−2bc+c^2−2ac+2ab+a^2)$
$=(a^2+b^2+c^2+a^2+b^2+c^2+a^2+b^2+c^2+a^2+b^2+c^2)+(2ab+2bc+2ac-2ab−2bc+2ac+2ab−2bc−2ac−2bc−2ac+2ab)$
$=4a^2+4b^2+4c^2+4ab-4bc$