(3m^2+7m-1)-(m^2+2m-5)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions: (3m^2 + 7m - 1) - (m^2 + 2m - 5)

This article will guide you through the process of simplifying the polynomial expression: (3m^2 + 7m - 1) - (m^2 + 2m - 5)

Understanding the Problem

The expression involves subtracting two trinomials. We need to combine like terms to simplify it.

Step-by-Step Solution

1. Distribute the negative sign: The negative sign in front of the second trinomial changes the sign of each term inside the parentheses.

   (3m^2 + 7m - 1) - (m^2 + 2m - 5) = 3m^2 + 7m - 1 - m^2 - 2m + 5

2. Combine like terms: Identify terms with the same variable and exponent and combine their coefficients.

   • m^2 terms: 3m^2 - m^2 = 2m^2
   • m terms: 7m - 2m = 5m
   • Constant terms: -1 + 5 = 4

3. Write the simplified expression: The simplified expression is the sum of the combined terms:

   2m^2 + 5m + 4

Conclusion

Therefore, the simplified form of the polynomial expression (3m^2 + 7m - 1) - (m^2 + 2m - 5) is 2m^2 + 5m + 4.