Simplifying Algebraic Expressions: (a^2b–5ab+2ab^2)+(–4a^2b+3ab+5ab^2)
This article will guide you through simplifying the algebraic expression: (a^2b–5ab+2ab^2)+(–4a^2b+3ab+5ab^2).
Understanding the Basics
Before we start simplifying, let's understand a few key points about algebraic expressions:
 Like Terms: Terms with the same variables raised to the same powers are considered like terms. For example,
3ab
and5ab
are like terms, but2ab^2
and3ab
are not.  Combining Like Terms: We can add or subtract only like terms. When combining like terms, we simply add or subtract their coefficients.
Simplifying the Expression

Identify Like Terms:
 a^2b:
a^2b
and4a^2b
are like terms.  ab:
5ab
and3ab
are like terms.  ab^2:
2ab^2
and5ab^2
are like terms.
 a^2b:

Combine Like Terms:
 a^2b:
a^2b  4a^2b = 3a^2b
 ab:
5ab + 3ab = 2ab
 ab^2:
2ab^2 + 5ab^2 = 7ab^2
 a^2b:

Write the Simplified Expression: The simplified expression is 3a^2b  2ab + 7ab^2.
Conclusion
By identifying like terms and combining them, we have successfully simplified the expression. The process of combining like terms is a fundamental concept in algebra and is essential for solving more complex algebraic equations and inequalities.