(5a2 + 4ab – 3b2) – (–5ab + 4b2 + 3a2) =

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:

(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.

Step-by-Step Solution

1. 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)

2. 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

3. 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

4. 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.