\(a)\) \({\left( {x + y} \right)^2} + {\left( {x - y} \right)^2}\) \( = {x^2} + 2xy + {y^2} + {x^2} - 2xy + {y^2}\)\( = 2{x^2} + 2{y^2}\)
\(b)\) \(2\left( {x - y} \right)\left( {x + y} \right) + {\left( {x + y} \right)^2} + {\left( {x - y} \right)^2}\)
\( = {\left[ {\left( {x + y} \right) + \left( {x - y} \right)} \right]^2} = {\left( {2x} \right)^2} = 4{x^2}\)
\(c)\) \({\left( {x - y + z} \right)^2} + {\left( {z - y} \right)^2}\)\( + 2\left( {x - y + z} \right)\left( {y - z} \right)\)
\(= {\left( {x - y + z} \right)^2} + 2\left( {x - y + z} \right)\left( {y - z} \right) \)\(+ {\left( {y - z} \right)^2} \)\( = {\left[ {\left( {x - y + z} \right) + \left( {y - z} \right)} \right]^2} = {x^2} \)
Chú ý:
\(\eqalign{
& {\left( {z - y} \right)^2} = {z^2} - 2zy + {y^2}\,\,\,(1) \cr
& {\left( {y - z} \right)^2} = {y^2} - 2yz + {z^2}\,\,\,(2) \cr
& \text{Từ (1) và (2)} \Rightarrow {\left( {z - y} \right)^2} = {\left( {y - z} \right)^2} \cr} \)
