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

Jasonbradley

2 min read

·

Jun 16, 2024

27

Share

Simplifying Algebraic Expressions: (a^2-3ab+b^2)+(-a^2+ab+b^2)

This article will guide you through the process of simplifying the algebraic expression: (a^2-3ab+b^2)+(-a^2+ab+b^2).

Understanding the Expression

The expression consists of two sets of terms enclosed in parentheses:

• (a^2-3ab+b^2)
• (-a^2+ab+b^2)

Each term within the parentheses is a combination of variables (a and b) and constants (coefficients like -3).

Simplifying the Expression

To simplify this expression, we follow these steps:

1. Remove the parentheses: Since the expression involves addition between the two sets of terms, the parentheses do not change the order of operations. We can simply remove them:

   a^2 - 3ab + b^2 - a^2 + ab + b^2
   

2. Combine like terms: Identify terms with the same variables and exponents. Combine their coefficients:

   • a^2 terms: a^2 - a^2 = 0
   • ab terms: -3ab + ab = -2ab
   • b^2 terms: b^2 + b^2 = 2b^2

3. Write the simplified expression: Combine the simplified terms:

   0 - 2ab + 2b^2 
   

Final Simplified Expression

The simplified form of the expression (a^2-3ab+b^2)+(-a^2+ab+b^2) is -2ab + 2b^2.