Question 29: Simplify the following expressions: \( {\left( {a + b + c} \right)^2} + {\left( {a – b – c} \right)^2} + {( b – c – a)^2} + {\left( {c – a – b} \right)^2}\)

\(\begin{array}{*{20}{l}} {{{\left( {a + b + c} \right)}^2} + {{\left( {a – b – c} \ right)}^2} + {{\left( {b – c – a} \right)}^2} + {{\left( {c – a – b} \right)}^2}}\\ { = {a^2} + {b^2} + {c^2} + 2ab + 2ac + 2bc + {a^2} + {b^2} + {c^2} – 2ab – 2ac + 2bc}\ \ { + {a^2} + {b^2} + {c^2} – 2ab – 2bc + 2ac + {a^2} + {b^2} + {c^2} + 2ab – 2ac – 2bc }\\ { = 4{a^2} + 4{b^2} + 4{c^2}} \end{array}\)