If a + b + c = 2s, then the value of (s - a)² + (s - b)² + (s - c)² + s² will be-

Solution(By Examveda Team)

$$\eqalign{ & {\left( {s - a} \right)^2} + {\left( {s - b} \right)^2} + {\left( {s - c} \right)^2} + {s^2} \cr & = \left( {{s^2} + {a^2} - 2sa} \right) + \left( {{s^2} + {b^2} - 2sb} \right) + \cr & \,\,\,\,\,\,\left( {{s^2} + {c^2} - 2sc} \right) + {s^2} \cr & = 4{s^2} + ({a^2} + {b^2} + {c^2}) - 2s(a + b + c) \cr & = {(2s)^2} + ({a^2} + {b^2} + {c^2}) - \cr & \,\,\,\,\,\,(a + b + c)(a + b + c) \cr & = {(a + b + c)^2} + \left( {{a^2} + {b^2} + {c^2}} \right) - \cr & \,\,\,\,\,\,{(a + b + c)^2} \cr & = {a^2} + {b^2} + {c^2} \cr} $$