-%E2%80%93-(%E2%80%935ab-%2B-4b2-%2B-3a2)-%3D-a2-%2B-ab-%2B-(-b2).jpeg "(5a2 + 4ab – 3b2) – (–5ab + 4b2 + 3a2) = A2 + Ab + ( B2)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the algebraic expression: (5a² + 4ab – 3b²) – (–5ab + 4b² + 3a²) = a² + ab + (–b²)
Understanding the Basics
To simplify this expression, we need to understand the following concepts:
- Combining Like Terms: We can only add or subtract terms that have the same variable and exponent. For example, 5a² and 3a² are like terms, but 5a² and 4ab are not.
- Distributing the Negative Sign: When subtracting an entire expression in parentheses, we must distribute the negative sign to each term inside the parentheses.
Simplifying the Expression
Let's break down the simplification process step by step:
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Distribute the Negative Sign: (5a² + 4ab – 3b²) – (–5ab + 4b² + 3a²) = (5a² + 4ab – 3b²) + (5ab – 4b² – 3a²)
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Combine Like Terms: 5a² - 3a² + 4ab + 5ab - 3b² - 4b² = 2a² + 9ab - 7b²
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Final Result: 2a² + 9ab - 7b² ≠ a² + ab + (–b²)
The given equation is incorrect. The correct simplified expression is 2a² + 9ab - 7b².
Important Note:
Remember that the order of operations (PEMDAS/BODMAS) is crucial in simplifying algebraic expressions. Always ensure that you perform operations in the correct order: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right).