October 6, 2025

What Are Like Terms In Algebra

Q: Are constant numbers (like 5 and -3) considered like terms?

Yes, constants are considered like terms because they have no variable part. You can always combine them by adding or subtracting.

Q: Can terms with different variables be like terms?

No. To be like terms, the variables must be identical. For example, `4a` and `4b` are not like terms because one has the variable 'a' and the other has 'b'.

Q: Is 3x²y a like term with 2xy²?

No, they are not like terms. Although they have the same variables (x and y), the exponents for each variable are different. In the first term, x is squared, and in the second, y is squared.

Q: What is the main purpose of combining like terms?

The main purpose is to simplify an algebraic expression. Simplification makes the expression easier to work with, especially when solving equations or performing more advanced algebraic manipulations.

Learn the definition of like terms in algebra. Understand how to identify and combine terms with the same variables and exponents through clear examples.

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Defining Like Terms in Algebra

In algebra, like terms are terms that have the exact same variable part, meaning the same variable(s) raised to the same power(s). The numerical coefficients (the numbers in front of the variables) can be different. Essentially, they are 'of the same kind'.

Section 2: How to Identify Like Terms

To identify like terms, you must check two things for each term: the variable and its exponent. For terms to be 'like,' both of these components must match exactly. For example, `7x²` and `-2x²` are like terms because they both contain the variable 'x' raised to the power of 2. However, `7x` and `7x²` are not like terms because their exponents differ.

Section 3: A Practical Example

Consider the algebraic expression: `5x + 3y² - 2x + 6y² + 4`. In this expression, `5x` and `-2x` are like terms because they both have the variable 'x' to the power of 1. Similarly, `3y²` and `6y²` are like terms because they both have the variable 'y' to the power of 2. The constant `4` has no other constants to be combined with.

Section 4: Why Combining Like Terms is Important

Combining like terms is a fundamental process for simplifying algebraic expressions and equations. By adding or subtracting the coefficients of like terms, you can reduce a long, complex expression into a shorter, more manageable one. This simplification is a crucial first step in solving for the variable and understanding the relationships within an equation.

Frequently Asked Questions

Are constant numbers (like 5 and -3) considered like terms?

Can terms with different variables be like terms?

Is 3x²y a like term with 2xy²?

What is the main purpose of combining like terms?