How do you find the difference of the polynomials 4m, 5, 6m, 7, and 2n?

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To find the difference of the polynomials 4m, 5, 6m, 7, and 2n, we first need to clearly define what it means to find the difference of polynomials. In algebra, the difference of two polynomials is obtained by subtracting them. However, in this case, we want to find the combined difference of multiple terms.

Let’s break down the polynomials we have:

  • 4m
  • 5
  • 6m
  • 7
  • 2n

To find the overall difference, we would typically want to group like terms together. This involves rewriting the expression to show how we’re combining these terms. Here, we separate the terms with ‘m’, constant terms, and the ‘n’ term:

  • Like terms in variable m: 4m and 6m
  • Constant terms: 5 and 7
  • Term with variable n: 2n

A step-by-step approach to find the difference of the given expression could be:

  1. Group the like terms for each variable:
  2. Combine the ‘m’ terms:
    • 4m – 6m = -2m
  3. Combine the constant terms:
    • 5 – 7 = -2
  4. Include the term with ‘n’:
    • -2n (remains unchanged)

Putting all this together, the final expression for the difference of the polynomials 4m, 5, 6m, 7, and 2n is:

Final result:

-2m – 2 + 2n

This simplified form gives you the overall difference while maintaining clarity and grouping like terms accurately. Thus, we’ve effectively calculated the difference while adhering to algebraic principles.

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