Answer
$(x+y)(x^2-xy+y^2+x-y)$
Work Step by Step
The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$.
The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$.
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
Hence here: $x^3+y^3+x^2-y^2=\\=(x+y)(x^2-xy+y^2)+(x+y)(x-y)\\=(x+y)(x^2-xy+y^2+x-y)$
