If a + b + c = 2s, then find the value of:
(s – a)³ + (s – b)³ + 3(s – a)(s – b)(c)

a + b + c = 2s

Expression to simplify: $$(s - a)^3 + (s - b)^3 + 3(s - a)(s - b)c$$​​

The given expression resembles the identity for the sum of cubes:

​$$x^3 + y^3 + 3xy(z) = (x + y)^3$$​​

where x = (s - a), y = (s - b), and z = c.

Let x = s - a and y = s - b. The expression becomes:

​$$(s - a)^3 + (s - b)^3 + 3(s - a)(s - b)c = x^3 + y^3 + 3xyc$$​​

By the identity, this simplifies to:

​$$(x + y)^3 = (s - a + s - b)^3$$​​

Now,

x + y = (s - a) + (s - b) = 2s - (a + b)

Using a + b + c = 2s, we get:

a + b = 2s - c

So:

x + y = 2s - (2s - c) = c

So, $$(x + y)^3 = c^3$$​​

Therefore, the value of the expression is $$\bf c^3.$$​​