Hi sweetkitten.
Remove brackets from 1st term and then do the same for the second but you must change signs. Then add and subtract like terms leaving unlikes as is
I agree with the teachers answer.I have explained how to do it. It requires you to change the signs in each of the terms in the second group.Forexample you have an x^3 in the first group and a -2x^3 in the second .These are like terms and added make a - x^3 the first term in the answer. You do this for the remaining terms and should get the right answer if you are careful with signs. Unlike terms appear in the answer (right signs )
(x^3-y^3)-(2x^3+x^2y-xy^2-2y^3)
Okay what happens is that in the second part you have to distribute the negative sign.
This expression becomes the same as:
(x^3 - y^3) -1(2x^3 + x^2y -xy^2 - 2y^3) Now distribute the negative sign
(x^3 - y^3 ) - 2x^3 - x^2y +xy^2 + 2y^3 Now remove the other set of brackets
x^3 - y^3 - 2x^3 - x^2y +xy^2 + 2y^3 Now simplify
-x^3 +y^3 - x^2y +xy^2 That's it.