Simplifying Algebraic Expressions: (a^2  3ab + 2b^2) + (4a^2 + 5ab  b^2)
This article will guide you through the process of simplifying the algebraic expression: (a^2  3ab + 2b^2) + (4a^2 + 5ab  b^2).
Understanding the Expression
The given expression involves addition of two trinomials. Trinomials are algebraic expressions with three terms.
Simplifying the Expression
To simplify this expression, we need to combine like terms:

Identify like terms: Look for terms with the same variables raised to the same powers.
 a² terms: a² and 4a²
 ab terms: 3ab and 5ab
 b² terms: 2b² and b²

Combine the coefficients of like terms:
 (a²  4a²) + (3ab + 5ab) + (2b²  b²)

Simplify:
 3a² + 2ab + b²
Final Answer
Therefore, the simplified form of the expression (a^2  3ab + 2b^2) + (4a^2 + 5ab  b^2) is 3a² + 2ab + b².