The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. if one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?

You need  to subtract the given addend from the sum:-

8d5 - 3c3d2 + 5c2d3 - 4cd4 + 9 - (2d5 - c3d2 + 8cd4 + 1)

Now we remove the parentheses - Note that the signs of the terms in the parentheses change because of the negative in front of the paranthese):_

 8d5 - 3c3d2 + 5c2d3 - 4cd4 + 9 - 2d5 + c3d2 - 8cd4 - 1

Now adding like term we get

6d5 - 2c3d2 + 5c2d3 - 12cd4 + 8

This is the other addend