Simplifying Algebraic Expressions
This article will guide you through the process of simplifying the algebraic expression:
(5a² + 4ab – 3b²) – (–5ab + 4b² + 3a²)
Understanding the Basics
 Terms: An algebraic expression consists of terms separated by addition or subtraction.
 Like Terms: Terms with the same variables raised to the same powers.
 Combining Like Terms: To simplify an expression, we combine like terms by adding or subtracting their coefficients.
StepbyStep Solution

Distribute the Negative Sign: Remember that subtracting an expression is the same as adding its negative. So, we distribute the negative sign in front of the second set of parentheses:
(5a² + 4ab – 3b²) + (5ab – 4b² – 3a²)

Identify Like Terms: Now, let's identify the like terms in the expression:
 a² terms: 5a² and 3a²
 ab terms: 4ab and 5ab
 b² terms: 3b² and 4b²

Combine Like Terms: Combine the coefficients of each set of like terms:
 a² terms: 5a²  3a² = 2a²
 ab terms: 4ab + 5ab = 9ab
 b² terms: 3b²  4b² = 7b²

Write the Simplified Expression: Combine the results to get the simplified expression:
2a² + 9ab – 7b²
Conclusion
By applying the principles of combining like terms, we successfully simplified the expression (5a² + 4ab – 3b²) – (–5ab + 4b² + 3a²) to 2a² + 9ab – 7b². Remember to always distribute negative signs and combine only like terms.