Question

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)\\)\\(\bigcirc\\ 6r^6s^3 - 4r^5s^4 + 7r^4s^5\\)\\(\bigcirc\\ 6r^6s^3 - 13r^5s^4 - r^4s^5\\)\\(\bigcirc\\ 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6\\)\\(\bigcirc\\ 8r^6s^3 - 13r^5s^4 + r^4s^5 - 5r^3s^6\\)

Explanation:

Step1: Distribute the negative sign

We have \((8r^{6}s^{3}-9r^{5}s^{4}+3r^{4}s^{5})-(2r^{4}s^{5}-5r^{3}s^{6}-4r^{5}s^{4})\). When we distribute the negative sign to the terms inside the second parentheses, we get:
\(8r^{6}s^{3}-9r^{5}s^{4}+3r^{4}s^{5}-2r^{4}s^{5}+5r^{3}s^{6}+4r^{5}s^{4}\)

Step2: Combine like terms

• For the \(r^{6}s^{3}\) term: There is only \(8r^{6}s^{3}\), so it remains as is.
• 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: \(3r^{4}s^{5}-2r^{4}s^{5}=r^{4}s^{5}\)
• For the \(r^{3}s^{6}\) term: There is only \(5r^{3}s^{6}\), so it remains as is.

Putting it all together, we have \(8r^{6}s^{3}-5r^{5}s^{4}+r^{4}s^{5}+5r^{3}s^{6}\)

Answer:

\(8r^{6}s^{3}-5r^{5}s^{4}+r^{4}s^{5}+5r^{3}s^{6}\) (the third option)