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2x^{2}+xy+y^{2}-xy+y^{2}
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}+y^{2}+y^{2}
Combine xy and -xy to get 0.
2x^{2}+2y^{2}
Combine y^{2} and y^{2} to get 2y^{2}.
2x^{2}+2y^{2}
Multiply and combine like terms.
2\left(x^{2}+y^{2}\right)
Factor out 2.