(2a+3b-5ab)+(5a-4b+2ab)-(7a+b-ab)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions

This article will guide you through the process of simplifying the algebraic expression:

(2a + 3b - 5ab) + (5a - 4b + 2ab) - (7a + b - ab)

Understanding the Basics

Before we begin, let's recap some fundamental concepts:

• Terms: Parts of an algebraic expression separated by addition or subtraction signs.
• Like Terms: Terms that have the same variables and exponents. (e.g., 2a and 5a are like terms, while 2a and 2b are not).
• Combining Like Terms: We can combine like terms by adding or subtracting their coefficients.

Simplifying the Expression

1. Remove Parentheses: Since we have addition and subtraction between the parentheses, we can simply remove them:

   2a + 3b - 5ab + 5a - 4b + 2ab - 7a - b + ab

2. Identify Like Terms: Now, group the like terms together:

   (2a + 5a - 7a) + (3b - 4b - b) + (-5ab + 2ab + ab)

3. Combine Like Terms: Add or subtract the coefficients of each group of like terms:

   (0a) + (-2b) + (-2ab)

4. Simplify: The final simplified expression is:

   -2b - 2ab

Conclusion

By applying the principles of combining like terms, we successfully simplified the given algebraic expression. This process allows us to represent complex expressions in a more concise and manageable form.