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Addition and Subtraction of Algebraic Expressions: Unraveling the Basics
In the world of algebra, mastering the art of adding and subtracting expressions is fundamental. Let’s dive into the basics of these operations to uncover the rules and techniques that make algebraic arithmetic a powerful tool.
1. Addition of Algebraic Expressions
Like Terms in Addition
When adding algebraic expressions, focus on combining like terms. Like terms have the same variable and exponent.
3x+2x=5x
7y−2y=5y
Addition with Constants
Combine constants just like you would with variables.
4+2=6
8a + 5a = 13a
2. Subtraction of Algebraic Expressions
Subtracting Like Terms
Similar to addition, subtract like terms by considering the signs.
5x−2x=3x
9p – 4p = 5p
Subtracting Constants
Subtract constants as you would in regular arithmetic.
10−3=7
6b – 2b = 4b
3. Combining Unlike Terms
When Like Terms Are Absent
If expressions have different variables or exponents, they cannot be combined directly.
2x+3y(cannot be combined)
Dealing with Negatives
When subtracting, distribute the negative sign to all terms in the second expression and proceed with addition.
4−(2a−3b) = 4−2a+3b
4. Practical Tips for Addition and Subtraction
Maintaining Order
In expressions, maintain the order of terms during addition and subtraction to avoid errors.
Simplification
Simplify expressions by combining like terms to make them more manageable and easier to understand.
5. Common Mistakes to Avoid
Forgetting Signs
Pay close attention to signs when combining terms. Adding a positive and negative term requires careful consideration.
Misplacing Terms:
Maintain the order of terms to prevent misplacement during calculations.
