Pre Algebra Like Terms Worksheet with Answers Key

Understanding how to simplify expressions by combining like terms is a fundamental skill in pre-algebra and algebra. This process helps students grasp the concept of variables and constants in a more practical way. Today, we'll dive deep into what like terms are, why they matter, and how to handle them through a comprehensive worksheet with an answers key for practice.

What Are Like Terms?

Like terms refer to terms that have the same variable raised to the same power. For example:

• 2x and 5x are like terms because both have the same variable x with no exponents.
• 3y² and -8y² are also like terms since both have the variable y raised to the second power.

Constants or numbers alone like 7 and 12 are also considered like terms because they can be combined to form a new constant.

Why Combine Like Terms?

Combining like terms simplifies expressions, making them easier to solve or understand:

• It reduces the complexity of an algebraic expression.
• Simplification can often reveal the structure of an equation, making it more manageable.
• It’s crucial for solving linear and polynomial equations.

How to Combine Like Terms: A Step-by-Step Guide

Here’s how you can approach combining like terms:

1. Identify Like Terms: Look for terms with the same variables and exponents.
2. Add or Subtract Coefficients: Combine the coefficients of the like terms while keeping the variable part unchanged.
3. Combine Constants: If there are numbers without variables, combine these as well.

Let’s see this in action with an example:

Example:

Simplify the expression: 4x + 2y - 3x + 7y - 1

• Identify like terms: 4x and -3x, 2y and 7y, and the constants -1.
• Combine coefficients:
  • x terms: 4x - 3x = 1x
  • y terms: 2y + 7y = 9y
  • Constants: -1 + 0 = -1
• Result: 1x + 9y - 1 or simply x + 9y - 1

Worksheet: Combining Like Terms

Now, let’s practice with a worksheet. Here are some expressions for you to simplify by combining like terms:

1. 3a + 4b - 2a + b
2. 5xy - 3xy + 7y - 2
3. -8m + 12m - 5n + n
4. 6 + 3a - 2b - 5 + a + 4b
5. 9t - 4 + t - 1

Answers Key

1. a + 5b
2. 2xy + 7y - 2
3. 4m - 4n
4. 4a + 2b + 1
5. 10t - 5

🔍 Note: Always simplify step-by-step and check your work to ensure accuracy.

Combining like terms isn't just about simplifying expressions; it's about understanding the algebra behind it, making problem-solving more straightforward. This practice not only reinforces basic algebraic concepts but also prepares students for more advanced topics where combining terms is a routine operation.

By mastering the process of combining like terms, you develop a clearer vision of how variables interact within an expression, which can lead to quicker and more efficient solutions in algebra and beyond. Remember, algebra isn't just about numbers and variables; it's about understanding the logical flow of mathematical operations, where each step builds upon the previous, much like the structure of this article.

Why do we combine like terms?

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Combining like terms simplifies algebraic expressions, making them easier to work with. It also helps in solving equations by reducing the number of terms you need to handle.

What happens if terms are not like?

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If terms are not like, they cannot be combined. They remain separate within the expression. For example, 2x and 3y are not like terms because they have different variables.

Can we combine like terms with different coefficients?

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Yes, as long as the variables and exponents match, you can add or subtract the coefficients to combine the terms. For example, 4a and 5a can be combined to 9a.

Is combining like terms only relevant for single variables?

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No, like terms can also include products of variables or terms with exponents. For instance, 2ab and 3ab are like terms, as are 4x² and -5x².