Question

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

Answer 1

The second polynomial is:

`6d^5-2c^3d^2+5c^2d^3-12cd^4+8`

Explanation:

Given

`Sum\ of\ polynomials=S=8d^5-3c^3d^2+5c^2d^3-4cd^4+9\\Polynomial\ 1=A=2d^5-c^3d^2+8cd^4+1\\Polynomial\ 2=B=?\\S=A+B\\B=S-A\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-(2d^5-c^3d^2+8cd^4+1)\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-2d^5+c^3d^2-8cd^4-1\\=8d^5-2d^5-3c^3d^2+c^3d^2+5c^2d^3-4cd^4-8cd^4+9-1\\=6d^5-2c^3d^2+5c^2d^3-12cd^4+8`