Simplifying Algebraic Expressions: (7a + 4b)  (2a + 2b  3c)
This article will guide you through simplifying the algebraic expression: (7a + 4b)  (2a + 2b  3c).
Understanding the Basics
Before we dive into the simplification, let's recap some fundamental concepts:
 Terms: A term is a single number, variable, or a product of numbers and variables. In our expression, 7a, 4b, 2a, 2b, and 3c are all terms.
 Like Terms: Like terms have the same variables raised to the same power. For example, 7a and 2a are like terms, but 4b and 3c are not.
 Combining Like Terms: We can combine like terms by adding or subtracting their coefficients. For example, 7a  2a = 5a.
Simplifying the Expression

Distribute the negative sign:
Remember that subtracting an expression is the same as adding its opposite. So, we can rewrite the expression as: (7a + 4b) + (2a  2b + 3c) 
Combine like terms:
 a terms: 7a  2a = 5a
 b terms: 4b  2b = 2b
 c terms: 3c remains unchanged

Write the simplified expression: The simplified expression is: 5a + 2b + 3c
Conclusion
By following these steps, we successfully simplified the algebraic expression (7a + 4b)  (2a + 2b  3c) to 5a + 2b + 3c. Remember to always distribute the negative sign and combine like terms for accurate simplification.