Sure, let's find the difference of these two polynomials step-by-step.
We start with:
[tex]\[
\left(8 r^6 s^3-9 r^5 s^4+3 r^4 s^5\right)-\left(2 r^4 s^5-5 r^3 s^6-4 r^5 s^4\right)
\][/tex]
First, distribute the negative sign through the second polynomial:
[tex]\[
8 r^6 s^3-9 r^5 s^4+3 r^4 s^5 - 2 r^4 s^5 + 5 r^3 s^6 + 4 r^5 s^4
\][/tex]
Now, combine like terms:
- For the term [tex]\(r^6 s^3\)[/tex]:
[tex]\[
8 r^6 s^3
\][/tex]
- For the term [tex]\(r^5 s^4\)[/tex]:
[tex]\[
-9 r^5 s^4 + 4 r^5 s^4 = -5 r^5 s^4
\][/tex]
- For the term [tex]\(r^4 s^5\)[/tex]:
[tex]\[
3 r^4 s^5 - 2 r^4 s^5 = r^4 s^5
\][/tex]
- For the term [tex]\(r^3 s^6\)[/tex]:
[tex]\[
5 r^3 s^6
\][/tex]
Putting it all together, we get:
[tex]\[
8 r^6 s^3 - 5 r^5 s^4 + r^4 s^5 + 5 r^3 s^6
\][/tex]
So, the difference of the polynomials is:
[tex]\[
\boxed{8 r^6 s^3-5 r^5 s^4+r^4 s^5+5 r^3 s^6}
\][/tex]
