#### Answer

$3x^{2}-3xy+6y^{2}$

#### Work Step by Step

We are asked to add the polynomials $(x^{2}+xy-y^{2})$ and $(2x^{2}-4xy+7y^{2})$.
This is equivalent to $(x^{2}+xy-y^{2})+(2x^{2}-4xy+7y^{2})$. We can combine like terms to add these polynomials together.
$(x^{2}+2x^{2})+(xy-4xy)+(-y^{2}+7y^{2})=3x^{2}-3xy+6y^{2}$