What is the difference between the polynomials 8r^6s^3, 9r^5s^4, 3r^4s^5, 2r^4s^5, 5r^3s^6, and 4r^5s^4?

The difference between the polynomials 8r⁶s³, 9r⁵s⁴, 3r⁴s⁵, 2r⁴s⁵, 5r³s⁶, and 4r⁵s⁴ involves identifying the unique terms, organizing them, and understanding their coefficients and exponents.

To find the difference between these polynomials, we need to first combine like terms. In this case, we can group the terms based on their expressions involving ‘r’ and ‘s’:

• 8r⁶s³
• (9r⁵s⁴ + 4r⁵s⁴ = 13r⁵s⁴)
• (3r⁴s⁵ + 2r⁴s⁵ = 5r⁴s⁵)
• 5r³s⁶

Therefore, the simplified polynomial combining like terms will be:

8r⁶s³ + 13r⁵s⁴ + 5r⁴s⁵ + 5r³s⁶.

So the difference essentially lies in how these terms are combined and expressed, emphasizing the importance of organizing polynomials correctly for further calculations.