Answer:
![-3x^4+3x^3+8x^2-2x-5](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qbnnzie3looq3k8dgt20bsrifyxve3s0nr.png)
Explanation:
Here we need to move the negative sign to the rest of the variables, and then only add the ones with the same power:
![(-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)\\-2x^4-2x^3+8x^2+2 - x^4+5x^3-2x-7](https://img.qammunity.org/2020/formulas/mathematics/middle-school/m40p3ie8e5yj2kzy2ce4peztyqe10rdxt6.png)
And then move the variables with the same power closer together
![-2x^4-x^4-2x^3+5x^3+8x^2-2x+2-7](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jyfwvsp77tyd5tz1m32f6ef59k89qteppn.png)
See how -x^4 and -2x^4 are together?
All we have to do now is combine.
![-2x^4-x^4-2x^3+5x^3+8x^2-2x+2-7\\-3x^4+3x^3+8x^2-2x-5](https://img.qammunity.org/2020/formulas/mathematics/middle-school/n6zz1v8laju3crv68ernvd6qw5a8qd7qvn.png)
So our answer is
![-3x^4+3x^3+8x^2-2x-5](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qbnnzie3looq3k8dgt20bsrifyxve3s0nr.png)