(a^2+b^2+c^2+2ab+2ac+2bc)^2
You asked:
Evaluate the expression: \({\left( {a}^{2} + {b}^{2} + {c}^{2} + 2 a b + 2 a c + 2 b c \right)}^{2}\)
MathBot Answer:
\[{\left( {a}^{2} + {b}^{2} + {c}^{2} + 2 a b + 2 a c + 2 b c \right)}^{2} = \left(a^{2} + 2 a b + 2 a c + b^{2} + 2 b c + c^{2}\right)^{2}\]
Expanded
\[{\left( {a}^{2} + {b}^{2} + {c}^{2} + 2 a b + 2 a c + 2 b c \right)}^{2} = a^{4} + 4 a^{3} b + 4 a^{3} c + 6 a^{2} b^{2} + 12 a^{2} b c + 6 a^{2} c^{2} + 4 b^{3} a + 12 b^{2} a c + 12 c^{2} a b + 4 c^{3} a + b^{4} + 4 b^{3} c + 6 b^{2} c^{2} + 4 c^{3} b + c^{4}\]
Factored
\[{\left( {a}^{2} + {b}^{2} + {c}^{2} + 2 a b + 2 a c + 2 b c \right)}^{2} = \left(a + b + c\right)^{4}\]