Question

Срочно ! Помогите пожалуйста КТО СМОЖЕТ !: (a + b + c)^2 + (a - b - c)^2 +( b - c - a) ^2 + (c - a - b)^2

Answer 1

Ответом будет - 4а^2+4b^2+4c^2
лучшая благодарность за помощь -отметка моего решения как лучшего:)

Answer 2

Let's simplify the expression step by step.

First, let's expand the squares using the formula:

(a + b)^2 = a^2 + 2ab + b^2

We have:

(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac

(a - b - c)^2 = a^2 + b^2 + c^2 - 2ab - 2bc + 2ac

(b - c - a)^2 = a^2 + b^2 + c^2 - 2ab + 2bc - 2ac

(c - a - b)^2 = a^2 + b^2 + c^2 + 2ab - 2bc - 2ac

Next, let's add up all the terms:

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

= 4(a^2 + b^2 + c^2)

Notice that all the cross terms with coefficients of 2 (i.e., 2ab, 2ac, 2bc) cancel out, leaving only the squared terms. This simplifies the expression significantly.

Therefore, the final answer is 4(a^2 + b^2 + c^2).