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

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)

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

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.