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(m^2+7mn-5n^2 )-(-2m^2+5mn-3n^2)

2 min read Jun 16, 2024
(m^2+7mn-5n^2 )-(-2m^2+5mn-3n^2)

Simplifying Algebraic Expressions: (m^2 + 7mn - 5n^2) - (-2m^2 + 5mn - 3n^2)

This article will guide you through simplifying the algebraic expression: (m^2 + 7mn - 5n^2) - (-2m^2 + 5mn - 3n^2).

Understanding the Concept

Simplifying algebraic expressions involves combining like terms. Like terms are terms that have the same variables raised to the same powers.

In this case, we have:

  • m^2 terms: m^2 and -2m^2
  • mn terms: 7mn and 5mn
  • n^2 terms: -5n^2 and -3n^2

Steps to Simplify

  1. Distribute the negative sign: Remember that subtracting a negative is the same as adding a positive. Therefore, we rewrite the expression as: (m^2 + 7mn - 5n^2) + (2m^2 - 5mn + 3n^2)

  2. Combine like terms: Now, group the like terms together: (m^2 + 2m^2) + (7mn - 5mn) + (-5n^2 + 3n^2)

  3. Simplify: Perform the arithmetic operations on the coefficients: 3m^2 + 2mn - 2n^2

Final Answer

Therefore, the simplified form of the algebraic expression (m^2 + 7mn - 5n^2) - (-2m^2 + 5mn - 3n^2) is 3m^2 + 2mn - 2n^2.

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