%2B(2a%5E2b%2B3ab%5E2-7ab).jpeg "(4a^2b-3ab^2+2ab+5)+(2a^2b+3ab^2-7ab)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the algebraic expression: (4a²b - 3ab² + 2ab + 5) + (2a²b + 3ab² - 7ab).
Understanding the Expression
The expression consists of two sets of terms enclosed in parentheses. Each set contains terms involving the variables a and b. Our goal is to combine like terms to simplify the expression.
Identifying Like Terms
Like terms are terms that have the same variables raised to the same powers. In our expression, we can identify the following like terms:
- a²b terms: 4a²b and 2a²b
- ab² terms: -3ab² and 3ab²
- ab terms: 2ab and -7ab
- Constant terms: 5 (this is the only constant term)
Combining Like Terms
Now, we can combine the like terms by adding their coefficients:
- a²b terms: 4a²b + 2a²b = 6a²b
- ab² terms: -3ab² + 3ab² = 0
- ab terms: 2ab - 7ab = -5ab
- Constant term: 5 remains unchanged
The Simplified Expression
Combining all the simplified terms, we get the final simplified expression:
6a²b - 5ab + 5
Summary
By identifying like terms and combining their coefficients, we have successfully simplified the original algebraic expression. This process is fundamental in algebra and allows us to manipulate expressions effectively for solving equations and other mathematical operations.