Question

Вывести формулы
a+b-c)^2
(a-b+c)^2
(a-b-c)^2

Answer 1

$(a+b-c)^2=Big ((a+b)-cBig )^2=(a+b)^2-2(a+b)cdot c+c^2=\\=a^2+2ab+b^2-2ac-2bc+c^2=a^2+b^2+c^2+2(ab-bc-ac)\\\(a-b+c)^2=Big ((a+c)-bBig )^2=(a+c)^2-2(a+c)cdot b+b^2=\\=a^2+2ac+c^2-2ab-2bc+b^2=a^2+b^2+c^2+2(ac-ab-bc)\\\(a-b-c)^2=Big (a-(b+c)Big )^2=a^2-2a(b+c)+(b+c)^2=\\=a^2-2ab-2ac+b^2+2bc+c^2=a^2+b^2+c^2+2(bc-ab-ac)$