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Simplifying Algebraic Expressions: (a²−3ab+2b²)+(−4a²+5ab−b²)
In this article, we will explore how to simplify the algebraic expression: (a²−3ab+2b²)+(−4a²+5ab−b²).
Understanding the Expression
This expression involves combining like terms. Like terms are terms that have the same variables raised to the same powers. For example:
- a² and -4a² are like terms because they both have the variable 'a' raised to the power of 2.
- -3ab and 5ab are like terms because they both have the variables 'a' and 'b' raised to the powers of 1.
- 2b² and -b² are like terms because they both have the variable 'b' raised to the power of 2.
Simplifying the Expression
To simplify the expression, we combine the like terms:
- Combine the a² terms: a² + (-4a²) = -3a²
- Combine the ab terms: -3ab + 5ab = 2ab
- Combine the b² terms: 2b² + (-b²) = b²
Therefore, the simplified expression is: -3a² + 2ab + b².
Key Takeaways
- Like terms are terms that have the same variables raised to the same powers.
- To simplify expressions, we combine like terms by adding or subtracting their coefficients.
- Remember to pay attention to the signs of the terms when combining them.
By understanding the concept of like terms and applying the rules of simplification, you can effectively simplify algebraic expressions like the one we explored in this article.