30+ FREE Combining Like Terms Worksheets (Pre Algebra, Linear, 6th Grade, 7th Grade, 8th Grade)
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Printable Combining Like Terms Worksheet
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Basic Combining Like Terms Worksheet
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Free Combining Like-Terms Worksheet
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Easy Combining Like Terms Worksheet
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Hard Combining Like-Terms Worksheet
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5th Grade Combining Like Terms Worksheet
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6th Grade Combining Like Terms Worksheet
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7th Grade Combining Like Terms Worksheet
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8th Grade Combining Like Terms Worksheet
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9th Grade Combining Like Terms Worksheet
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10th Grade Combining Like Terms Worksheet
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High School Combining Like Terms Worksheet
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Algebra Combining Like Terms Worksheet
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Algebraic Expressions Combining Like Terms Worksheet
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Combining Like Terms Activity Worksheet
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Combining Like Terms and Distributive Property Worksheet
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Dice Game Combining Like Terms Worksheet
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Distributive Property to Combining Like Terms and Worksheet
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Linear Equations Combining Like Terms Worksheet
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Mixed Combining Like Terms Worksheet
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Practice Basic Combining Like Terms Worksheet
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Practice Combining Like Terms Worksheet
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Pre Algebra Combining Like Terms Worksheet
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Primary Combining Like Terms Worksheet
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Sample Combining Like Terms Worksheet
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Simple Combining Like Terms Worksheet
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Simplifying Combining Like Terms Expressions Worksheet
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Simplifying Expressions Combining Like Terms Worksheet
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Solving Combining Like Terms Worksheet
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Word Combining Like Terms Worksheet
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What Are Like Terms?
In algebra, like terms are terms that have the same variable(s) raised to the same exponent. The coefficients (numerical values) of like terms can be added or subtracted, but the variables remain unchanged. This concept is essential for simplifying algebraic expressions and solving equations efficiently.
For example, in the expression 4x + 7x – 3y + 5y – 2, the like terms are:
- 4x and 7x (same variable “x”)
- -3y and 5y (same variable “y”)
By combining these like terms, the simplified expression becomes 11x + 2y – 2.
However, terms with different variables or exponents cannot be combined. For example, in 3x² + 4x + 2y, no terms are like terms because they have different variables or exponents.
Why Is Combining Like Terms Important?
Combining like terms is a fundamental skill in algebra that helps simplify equations and expressions. It allows students to:
- Simplifies expressions – Reduces the complexity of algebraic equations, making them easier to work with.
- Prepares for solving equations – Helps in isolating variables to solve for unknown values.
- Strengthens algebraic foundations – Essential for understanding polynomials, factoring, and algebraic operations.
- Improves problem-solving efficiency – Speeds up calculations and logical thinking in algebra.
- Applies to real-world problems – Helps in understanding financial calculations, measurements, and scientific formulas.
Mastering this concept builds a strong foundation for advanced math topics such as polynomials, factoring, and equation solving.
How to Identify Like Terms
To effectively combine like terms, follow these steps:
- Look at the variables and exponents – Like terms must have the exact same variable(s) and exponent(s).
- Check the coefficients – The numerical value in front of a variable can change, but the variable itself must be the same.
- Ignore constant terms – Numbers without variables (like -5 or 10) are separate and cannot be combined with variable terms.
Examples of Like and Unlike Terms
Expression | Like Terms | Unlike Terms |
---|---|---|
3x + 5x – 2y + 4y | 3x, 5x and -2y, 4y | x, y |
2a² + 4a + 3a² – 7a | 2a², 3a² and 4a, -7a | a², a |
6m³ – 4m + 2m³ + 5m | 6m³, 2m³ and -4m, 5m | m³, m |
How to Combine Like Terms
To combine like terms in an algebraic expression, follow these simple steps:
- Identify like terms – Look for terms that have the same variable(s) and exponent(s).
- Group the like terms – Rearrange the expression if necessary to place like terms together.
- Add or subtract the coefficients – Keep the variable unchanged while performing the arithmetic operation.
- Rewrite the simplified expression – Ensure that no further like terms exist.
For example, simplify the expression:
2x + 3y – 5x + 7y
Step 1: Identify like terms (2x and -5x, 3y and 7y)
Step 2: Combine like terms (2x – 5x = -3x, 3y + 7y = 10y)
Step 3: Final expression: -3x + 10y
Tips for Mastering Combining Like Terms
- Use color coding – Highlight like terms in different colors to visualize the grouping.
- Rewrite expressions neatly – Organize terms properly to avoid mistakes.
- Double-check signs – Pay attention to positive and negative coefficients.
- Practice with real-world examples – Apply like terms in shopping receipts, budgeting, and physics formulas.
- Work with peers – Solving problems with classmates helps reinforce understanding.