Simplifying Algebraic Expressions: (a^23ab+b^2)+(a^2+ab+b^2)
This article will guide you through the process of simplifying the algebraic expression: (a^23ab+b^2)+(a^2+ab+b^2).
Understanding the Expression
The expression consists of two sets of terms enclosed in parentheses:
 (a^23ab+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:

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

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

Write the simplified expression: Combine the simplified terms:
0  2ab + 2b^2
Final Simplified Expression
The simplified form of the expression (a^23ab+b^2)+(a^2+ab+b^2) is 2ab + 2b^2.