Final answer:
The difference of the polynomials 6x^6 - x^3y^4 - 5xy^5 and 4x^5y + 2x^3y^4 + 5xy^5 is 6x^6 - 3x^3y^4 - 4x^5y. This resulting polynomial has 3 terms and its highest degree term is x^6, indicating that it has a degree of 6. Thus, the difference has 3 terms and a degree of 6.
Step-by-step explanation:
To find the completely simplified difference between the two polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5, we subtract the second polynomial from the first. This means we change the signs of the terms in the second polynomial and then combine like terms with the first polynomial.
Here's the subtraction step by step:
- 6x6 (no like term to subtract from, so it remains as is)
- −x3y4 − (2x3y4) = −x3y4 − 2x3y4 = −3x3y4
- −5xy5 − (−5xy5) = −5xy5 + 5xy5 = 0 (they cancel out)
- (Nothing to subtract from 4x5y, so this term is simply negated)
The resulting polynomial after subtracting is 6x6 − 3x3y4 − 4x5y. This polynomial has 3 terms and the highest degree term is x6, which makes it a degree of 6. Therefore, the correct statement is "The difference has 3 terms and a degree of 6."