%2B(2%2F5x%2B5-4y).jpeg "(1/5x-4+2y)+(2/5x+5-4y)")
Simplifying Algebraic Expressions: (1/5x - 4 + 2y) + (2/5x + 5 - 4y)
This article will guide you through the process of simplifying the algebraic expression: (1/5x - 4 + 2y) + (2/5x + 5 - 4y).
Understanding the Expression
The expression involves combining like terms, which are terms that have the same variables raised to the same powers. Let's break down the expression:
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(1/5x - 4 + 2y): This part contains three terms:
- (1/5x): A term with the variable 'x' raised to the power of 1.
- -4: A constant term.
- 2y: A term with the variable 'y' raised to the power of 1.
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(2/5x + 5 - 4y): This part also contains three terms:
- (2/5x): A term with the variable 'x' raised to the power of 1.
- 5: A constant term.
- -4y: A term with the variable 'y' raised to the power of 1.
Simplifying the Expression
To simplify, we'll combine like terms:
- Combine 'x' terms: (1/5x) + (2/5x) = (1+2)/5x = (3/5)x
- Combine 'y' terms: 2y - 4y = -2y
- Combine constant terms: -4 + 5 = 1
The Simplified Expression
Therefore, the simplified expression is: (3/5)x - 2y + 1
Conclusion
By combining like terms, we simplified the original expression into a more concise form: (3/5)x - 2y + 1. This process of simplification makes it easier to understand and work with the expression.