(7a+4b)-(2a+2b-3c)

Jasonbradley

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Jun 16, 2024

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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

1. 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)

2. Combine like terms:

   • a terms: 7a - 2a = 5a
   • b terms: 4b - 2b = 2b
   • c terms: 3c remains unchanged

3. 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.