Basic Combining Like Terms Worksheet

📆 Updated: 1 Jan 1970
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A basic combining like terms worksheet is a helpful tool for middle school or high school students learning algebraic expressions. These worksheets provide practice problems that allow students to familiarize themselves with identifying and simplifying expressions by combining similar terms.



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What is the purpose of combining like terms?

The purpose of combining like terms is to simplify algebraic expressions by grouping together terms that have the same variables raised to the same powers. By combining like terms, we can make the expression more concise and easier to work with, ultimately making it easier to solve equations and perform other operations in algebra.

How do you identify like terms in an expression?

To identify like terms in an expression, you look for terms that have the same variables raised to the same powers. For example, in the expression 3x + 2y - 5x - 4y, the terms 3x and -5x are like terms because they both have the variable x raised to the power of 1. Similarly, 2y and -4y are like terms because they both have the variable y raised to the power of 1. By identifying like terms, you can simplify expressions by combining them together.

Can constants be considered like terms?

No, constants cannot be considered like terms. Like terms are terms that have the same variables raised to the same powers, while constants are terms that do not include any variables. Therefore, constants do not have the same characteristics as like terms and are treated differently in algebraic expressions.

Give an example of an expression with like terms.

An example of an expression with like terms is: 2x + 3x - 5x. In this expression, all terms involve the variable x raised to the power of 1, making them like terms that can be combined by adding or subtracting their coefficients.

How do you combine like terms with the same variable?

To combine like terms with the same variable, you add or subtract the coefficients of those terms while keeping the variable the same. For example, if you have 3x + 2x, you combine these terms by adding the coefficients: 3x + 2x = 5x. Similarly, if you have 5y - 3y, you combine these terms by subtracting the coefficients: 5y - 3y = 2y. Just remember to always keep the variable the same when combining like terms.

Can you combine terms with different variables?

No, you cannot combine terms with different variables in algebraic expressions because they represent different quantities or unknowns. Each variable has its own unique value and cannot be combined with variables representing different values.

What is the result when you combine like terms?

When you combine like terms, you simplify an algebraic expression by adding or subtracting terms that have the same variable raised to the same power. This process helps to reduce the complexity of the expression and consolidate similar terms into one, resulting in a more concise and organized representation of the original expression.

Is the order of the terms important when combining like terms?

Yes, the order of terms is not important when combining like terms in an algebraic expression. Like terms are terms that have the same variables raised to the same powers, so they can be combined regardless of their order in the expression. The coefficients of the like terms can be added or subtracted to simplify the expression, regardless of their positions within the original expression.

What are the key steps to simplify an expression by combining like terms?

To simplify an expression by combining like terms, you need to first identify the terms that have the same variable and exponent. Next, you add or subtract the coefficients of these like terms to merge them into a single term. Arrange the simplified terms in descending order based on the variable's exponents. Finally, combine any constants that are left after simplification to achieve the simplest form of the expression.

Can you give an example of an expression that cannot be simplified by combining like terms?

An example of an expression that cannot be simplified by combining like terms is "3x^2 + 2y - 5x^2 + 4z." Since the terms have different variables (x, y, z), they cannot be combined or simplified further.

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