what is the difference of the polynomials? (8r^6s^3 - 9r^5s^4 + 3r^4s^5)-(2r^4s^5 - 5r^3s^6 - 4r^5s^4)…

what is the difference of the polynomials? (8r^6s^3 - 9r^5s^4 + 3r^4s^5)-(2r^4s^5 - 5r^3s^6 - 4r^5s^4) 6r^6s^3 - 4r^5s^4 + 7r^4s^5 6r^6s^3 - 13r^5s^4 - r^4s^5 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6 8r^6s^3 - 13r^5s^4 + r^4s^5 - 5r^3s^6

what is the difference of the polynomials? (8r^6s^3 - 9r^5s^4 + 3r^4s^5)-(2r^4s^5 - 5r^3s^6 - 4r^5s^4) 6r^6s^3 - 4r^5s^4 + 7r^4s^5 6r^6s^3 - 13r^5s^4 - r^4s^5 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6 8r^6s^3 - 13r^5s^4 + r^4s^5 - 5r^3s^6

Answer

Explanation:

Step1: Distribute the negative sign

$(8r^{6}s^{3}-9r^{5}s^{4}+3r^{4}s^{5})-(2r^{4}s^{5}-5r^{3}s^{6}-4r^{5}s^{4})=8r^{6}s^{3}-9r^{5}s^{4}+3r^{4}s^{5}-2r^{4}s^{5}+5r^{3}s^{6}+4r^{5}s^{4}$

Step2: Combine like - terms

For the $r^{5}s^{4}$ terms: $-9r^{5}s^{4}+4r^{5}s^{4}=-5r^{5}s^{4}$ For the $r^{4}s^{5}$ terms: $3r^{4}s^{5}-2r^{4}s^{5}=r^{4}s^{5}$ The expression becomes $8r^{6}s^{3}-5r^{5}s^{4}+r^{4}s^{5}+5r^{3}s^{6}$

Answer:

$8r^{6}s^{3}-5r^{5}s^{4}+r^{4}s^{5}+5r^{3}s^{6}$