%2B(4x%5E2-2y%2B6xy).jpeg "(-8xy+3x^2-5y)+(4x^2-2y+6xy)")
Simplifying Algebraic Expressions
This article will guide you through the process of simplifying the following algebraic expression:
(-8xy + 3x² - 5y) + (4x² - 2y + 6xy)
Understanding the Basics
Before we begin, let's refresh some key concepts:
- Terms: Parts of an algebraic expression separated by addition or subtraction signs. In our expression, we have terms like -8xy, 3x², -5y, 4x², -2y, and 6xy.
- Like Terms: Terms that have the same variables raised to the same powers. For example, 3x² and 4x² are like terms, while -8xy and 6xy are also like terms.
Combining Like Terms
To simplify the expression, we need to combine like terms. Here's how:
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Identify Like Terms: Group the terms with the same variables and powers together.
- x² terms: 3x² + 4x²
- xy terms: -8xy + 6xy
- y terms: -5y - 2y
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Combine Coefficients: Add or subtract the coefficients of like terms. Remember to pay attention to the signs!
- x² terms: (3 + 4)x² = 7x²
- xy terms: (-8 + 6)xy = -2xy
- y terms: (-5 - 2)y = -7y
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Write the Simplified Expression: Combine the simplified terms.
Therefore, the simplified expression is: 7x² - 2xy - 7y
Conclusion
By understanding the concepts of terms and like terms, we can efficiently combine similar elements within an algebraic expression. This process of simplification helps us express the same mathematical idea in a more compact and readable form.