To find the difference between the given polynomials, we need to look at the terms carefully. Let’s first rewrite the polynomials for clarity:
- 2x³y²
- 4x²y³
- 3xy⁴
- 6x⁴y
- 5x²y³y⁵
The difference between these polynomials can often involve finding the like terms and systematically subtracting coefficients associated with identical terms. However, it’s important to note that these polynomials have different degrees and may not combine easily.
For instance:
- 2x³y² is a term with degree 5 (3 from x and 2 from y).
- 4x²y³ is a degree 5 term as well.
- 3xy⁴ has a degree of 5 (1 from x and 4 from y).
- 6x⁴y is another degree 5 term.
- 5x²y³y⁵ simplifies to 5x²y⁸. This has a degree of 10 (2 from x and 8 from y).
Since they all differ either in their coefficients, variables, or degrees, these cannot be directly subtracted like simple arithmetic. Instead, the expression stands as a collection of these polynomials:
So, the combination goes as follows, without combining terms:
2x³y² – 4x²y³ – 3xy⁴ – 6x⁴y – 5x²y⁸
This representation shows their difference without further simplification due to their non-matching terms. Each part holds its value, and as they cannot combine, this will be the resultant expression.