Question

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

Answer 1

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

Answer 2

To correctly represent the formulas, I assume you meant to have an opening parenthesis before each of them. Below are the corrected expressions:

1. (a + b - c)^2
2. (a - b + c)^2
3. (a - b - c)^2

Each expression represents a square of the respective trinomial. If you need further explanation or have any specific questions about these formulas, feel free to ask!