The correct answer is C) The sum has a degree of 6, but the difference has a degree of 7.
In order to find the correct answer, we first have to find the sum and difference. We'll start with the sum.
3x^5y - 2x^3y^4 - 7xy^3 - 8x^5y + 2x^3y^4 + xy^3
By combining like terms we get the following.
-5x^5y -6xy^3
The term with the most amount of variables is the first one which has 5 x's and 1 y. As a result, it is a 6th degree polynomial.
For the difference, we have the following.
3x^5y - 2x^3y^4 - 7xy^3 - (-8x^5y + 2x^3y^4 + xy^3)
Which simplifies to
11x^5y - 4x^3y^4 -8xy^3
The term in this final simplification with the most variables is the second one, with 3 x's and 4 y's. As a result, there are 7 variables and it is a 7th degree.