(a^2-3ab+2b^2)+(-4a^2+5ab-b^2)

Jasonbradley

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Jun 16, 2024

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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:

1. 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

2. Combine the coefficients of like terms:

   • (a² - 4a²) + (-3ab + 5ab) + (2b² - b²)

3. 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.