Answer: The required difference is [tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
Step-by-step explanation: We are given to find the difference of the polynomials as follows :
[tex]DP=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the given difference, we need to choose the terms with same poers of the unknown variables r and s and then subtract their coefficients.
The difference (i) is as follows :
[tex]DP\\\\=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)\\\\=8r^6s^3-9r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6+4r^5s^4\\\\=8r^6s^3+(4-9)r^5s^4+(3-2)r^4s^5+5r^3s^6\\\\=8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
Thus, the required difference is [tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
