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How Can You Identify Like Terms in Algebraic Expressions?

Identifying like terms in algebra may seem tricky at first. But once you understand it, it gets easier and makes sense! In algebra, terms are the parts that make up expressions. Knowing how to spot them is important for simplifying and solving equations. Let's take a closer look at this important skill.

What is a Term?

A term is a single part of an algebra expression. It can be:

  • A number (like 3)
  • A variable (like x)
  • Or a mix of numbers and variables multiplied together.

For example, in the expression 5x + 3 - 2y + 7, we have four separate terms: 5x, 3, -2y, and 7.

What are Like Terms?

Like terms are terms that have the same variable and those variables are raised to the same power. This is important because you can add or subtract like terms.

For example, in the expression 4x + 2x, the terms 4x and 2x are like terms. They both have the variable x raised to the first power. You can combine them to get 6x.

Key Features of Like Terms

  1. Same Variable(s): The terms must have the same variables. For instance, 3xy and 4xy are like terms, but 3xy and 2x² are not.

  2. Same Exponents: The variables must have the same exponent. 5x² and 3x² are like terms since they both have x raised to the power of 2. But 5x² and 3x³ are not like terms because their exponents are different.

  3. No Addition of Different Variables: If there are different variables, the terms are not alike. For example, 2xy and 3x are not like terms because one has a y while the other does not.

Steps to Identify Like Terms

It takes some practice to identify like terms, but here’s a simple way to do it:

  • Step 1: Write down the expression clearly.
  • Step 2: Separate each term by addition (+) or subtraction (–).
  • Step 3: Look at each term and find the variables and their exponents.
  • Step 4: Group the terms that have the same variables and exponents.

Example to Practice

Let’s look at this expression:

2a + 3b + 5a - 7b + 4 + 6

  1. Identify the terms: The terms here are 2a, 3b, 5a, -7b, 4, and 6.

  2. Group the like terms:

    • 2a and 5a are like terms.
    • 3b and -7b are like terms.
    • The constants 4 and 6 are also like terms.
  3. Combine the like terms:

    • For a: 2a + 5a = 7a
    • For b: 3b - 7b = -4b
    • For the constants: 4 + 6 = 10

Putting it all together, the new expression is:

7a - 4b + 10

As you practice more, spotting like terms will get easier!

Practice Makes Perfect

Here are some exercises for you:

  1. Identify and combine the like terms in these expressions:

    • 4x + 3y - 2x + y
    • 5a² + 3b - 6a² + 4b + 7
    • 2xyz + 3x - xyz + 5y
  2. Find the like terms and simplify these expressions:

    • 7x² - 2x + 3x² + 4 - x + 9
    • 6mn + 3n - 4mn + 8p + 2n - 7

By practicing how to spot like terms, you’re building a strong base for other algebra skills, like factoring and working with polynomials.

Conclusion

Identifying like terms is a key math skill, especially for 8th graders. By knowing that like terms have the same variable and exponent, you can simplify expressions and solve problems better. Remember, practicing with different expressions is important, so keep working on these steps. Before you know it, spotting like terms will feel easy!

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How Can You Identify Like Terms in Algebraic Expressions?

Identifying like terms in algebra may seem tricky at first. But once you understand it, it gets easier and makes sense! In algebra, terms are the parts that make up expressions. Knowing how to spot them is important for simplifying and solving equations. Let's take a closer look at this important skill.

What is a Term?

A term is a single part of an algebra expression. It can be:

  • A number (like 3)
  • A variable (like x)
  • Or a mix of numbers and variables multiplied together.

For example, in the expression 5x + 3 - 2y + 7, we have four separate terms: 5x, 3, -2y, and 7.

What are Like Terms?

Like terms are terms that have the same variable and those variables are raised to the same power. This is important because you can add or subtract like terms.

For example, in the expression 4x + 2x, the terms 4x and 2x are like terms. They both have the variable x raised to the first power. You can combine them to get 6x.

Key Features of Like Terms

  1. Same Variable(s): The terms must have the same variables. For instance, 3xy and 4xy are like terms, but 3xy and 2x² are not.

  2. Same Exponents: The variables must have the same exponent. 5x² and 3x² are like terms since they both have x raised to the power of 2. But 5x² and 3x³ are not like terms because their exponents are different.

  3. No Addition of Different Variables: If there are different variables, the terms are not alike. For example, 2xy and 3x are not like terms because one has a y while the other does not.

Steps to Identify Like Terms

It takes some practice to identify like terms, but here’s a simple way to do it:

  • Step 1: Write down the expression clearly.
  • Step 2: Separate each term by addition (+) or subtraction (–).
  • Step 3: Look at each term and find the variables and their exponents.
  • Step 4: Group the terms that have the same variables and exponents.

Example to Practice

Let’s look at this expression:

2a + 3b + 5a - 7b + 4 + 6

  1. Identify the terms: The terms here are 2a, 3b, 5a, -7b, 4, and 6.

  2. Group the like terms:

    • 2a and 5a are like terms.
    • 3b and -7b are like terms.
    • The constants 4 and 6 are also like terms.
  3. Combine the like terms:

    • For a: 2a + 5a = 7a
    • For b: 3b - 7b = -4b
    • For the constants: 4 + 6 = 10

Putting it all together, the new expression is:

7a - 4b + 10

As you practice more, spotting like terms will get easier!

Practice Makes Perfect

Here are some exercises for you:

  1. Identify and combine the like terms in these expressions:

    • 4x + 3y - 2x + y
    • 5a² + 3b - 6a² + 4b + 7
    • 2xyz + 3x - xyz + 5y
  2. Find the like terms and simplify these expressions:

    • 7x² - 2x + 3x² + 4 - x + 9
    • 6mn + 3n - 4mn + 8p + 2n - 7

By practicing how to spot like terms, you’re building a strong base for other algebra skills, like factoring and working with polynomials.

Conclusion

Identifying like terms is a key math skill, especially for 8th graders. By knowing that like terms have the same variable and exponent, you can simplify expressions and solve problems better. Remember, practicing with different expressions is important, so keep working on these steps. Before you know it, spotting like terms will feel easy!

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