What is the difference between the two polynomials 7y² and 6xy and 2xy and 3?

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To find the difference between the polynomials 7y², 6xy, 2xy, and 3, we first need to identify which polynomials we are comparing and how to express this difference mathematically.

Let’s break this down step-by-step:

  1. Identify the Polynomials:
    • Polynomial 1: 7y²
    • Polynomial 2: 6xy
    • Polynomial 3: 2xy
    • Polynomial 4: 3
  2. Organize the Polynomials: If we are looking for the difference, we generally denote it in the following way:
    3.     Difference = (Polynomial 1) - (Polynomial 2) - (Polynomial 3) - (Polynomial 4)
  3. Calculate the Difference:
    4.     Difference = 7y² - 6xy - 2xy - 3
  4. Simplify the Expression: Now we combine like terms where possible.
    5.     Difference = 7y² - (6xy + 2xy) - 3

    Combining the xy terms gives us:

        Difference = 7y² - 8xy - 3

Final Expression: The final expression representing the difference among the polynomials is:

7y² - 8xy - 3

This expression illustrates how the polynomials differ in their components. It is important to recognize the signs and ensure each component is accurately represented during the calculation.

In summary, the difference between the polynomials 7y², 6xy, 2xy, and 3 leads us to the expression:

7y² - 8xy - 3

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