Combining Like Terms in the Given Expression

Oct 13, 2025 by windailys.com 29 views

Introduction

In algebra, combining like terms is a fundamental concept that helps simplify complex expressions. It involves adding or subtracting terms that have the same variable raised to the same power. In this article, we will focus on combining like terms in a given expression and provide a step-by-step guide on how to do it.

What are Like Terms?

Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. Similarly, $3y^2$ and $4y^2$ are like terms because they both have the variable $y$ raised to the power of 2.

Combining Like Terms in the Given Expression

The given expression is $\frac{3}{4} a + 8 - \frac{1}{4} a - 2$ . To combine like terms, we need to identify the like terms in the expression. In this case, the like terms are $\frac{3}{4} a$ and $-\frac{1}{4} a$ , which both have the variable $a$ raised to the power of 1.

Step 1: Combine the Like Terms

To combine the like terms, we need to add or subtract their coefficients. In this case, we need to add the coefficients of $\frac{3}{4} a$ and $-\frac{1}{4} a$ . The coefficient of $\frac{3}{4} a$ is $\frac{3}{4}$ , and the coefficient of $-\frac{1}{4} a$ is $-\frac{1}{4}$ .

from fractions import Fraction

# Define the coefficients of the like terms
coefficient1 = Fraction(3, 4)
coefficient2 = Fraction(-1, 4)

# Add the coefficients
combined_coefficient = coefficient1 + coefficient2

print(combined_coefficient)

The output of the above code is $\frac{1}{2}$ . Therefore, the combined coefficient of the like terms is $\frac{1}{2}$ .

Step 2: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by adding or subtracting the constants. In this case, we need to add the constants $8$ and $-2$ .

# Define the constants
constant1 = 8
constant2 = -2

# Add the constants
simplified_constant = constant1 + constant2

print(simplified_constant)

The output of the above code is $6$ . Therefore, the simplified expression is $\frac{1}{2} a + 6$ .

Conclusion

In this article, we have learned how to combine like terms in a given expression. We have identified the like terms, combined their coefficients, and simplified the expression. By following these steps, we can simplify complex algebraic expressions and make them easier to work with.

Example Problems

Here are some example problems that you can try to practice combining like terms:

Combine the like terms in the expression $2x + 5y - 3x - 2y$ .
Combine the like terms in the expression $\frac{1}{2} a + 4 - \frac{1}{2} a - 3$ .
Combine the like terms in the expression $3x^2 + 2y^2 - 2x^2 - 3y^2$ .

Answer Key

Here are the answers to the example problems:

The combined expression is $-x + 3y$ .
The combined expression is $4 - 3$ .
The combined expression is $x^2 - y^2$ .

Tips and Tricks

Here are some tips and tricks that you can use to help you combine like terms:

Identify the like terms in the expression by looking for terms that have the same variable raised to the same power.
Combine the coefficients of the like terms by adding or subtracting them.
Simplify the expression by adding or subtracting the constants.
Use the distributive property to expand expressions and make it easier to combine like terms.
Use the commutative property to rearrange terms and make it easier to combine like terms.

Introduction

Combining like terms is a fundamental concept in algebra that helps simplify complex expressions. In our previous article, we provided a step-by-step guide on how to combine like terms. In this article, we will answer some frequently asked questions about combining like terms and provide additional tips and tricks to help you become more proficient in this skill.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. Similarly, $3y^2$ and $4y^2$ are like terms because they both have the variable $y$ raised to the power of 2.

Q: How do I identify like terms in an expression?

A: To identify like terms in an expression, look for terms that have the same variable raised to the same power. For example, in the expression $2x + 5y - 3x - 2y$ , the like terms are $2x$ and $-3x$ because they both have the variable $x$ raised to the power of 1. Similarly, the like terms are $5y$ and $-2y$ because they both have the variable $y$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients. For example, in the expression $2x + 5y - 3x - 2y$ , the like terms are $2x$ and $-3x$ . To combine them, add their coefficients: $2 - 3 = -1$ . Therefore, the combined expression is $-x + 5y - 2y$ .

Q: What is the order of operations when combining like terms?

A: When combining like terms, the order of operations is:

Identify the like terms in the expression.
Combine the coefficients of the like terms by adding or subtracting them.
Simplify the expression by adding or subtracting the constants.

Q: Can I combine like terms with different variables?

A: No, you cannot combine like terms with different variables. For example, in the expression $2x + 5y - 3x - 2y$ , you cannot combine the terms $2x$ and $5y$ because they have different variables.

Q: Can I combine like terms with different exponents?

A: No, you cannot combine like terms with different exponents. For example, in the expression $2x^2 + 5y^2 - 3x^2 - 2y^2$ , you cannot combine the terms $2x^2$ and $5y^2$ because they have different exponents.

Q: What are some common mistakes to avoid when combining like terms?

A: Some common mistakes to avoid when combining like terms include:

Not identifying like terms in the expression.
Not combining the coefficients of like terms correctly.
Not simplifying the expression after combining like terms.
Combining like terms with different variables or exponents.

Conclusion

Combining like terms is a fundamental concept in algebra that helps simplify complex expressions. By following the steps outlined in this article and avoiding common mistakes, you can become more proficient in combining like terms and simplifying algebraic expressions.

Additional Resources

Here are some additional resources that you can use to learn more about combining like terms:

Khan Academy: Combining Like Terms
Mathway: Combining Like Terms
IXL: Combining Like Terms

Practice Problems

Here are some practice problems that you can use to practice combining like terms:

Combine the like terms in the expression $2x + 5y - 3x - 2y$ .
Combine the like terms in the expression $\frac{1}{2} a + 4 - \frac{1}{2} a - 3$ .
Combine the like terms in the expression $3x^2 + 2y^2 - 2x^2 - 3y^2$ .

Answer Key

Here are the answers to the practice problems:

The combined expression is $-x + 5y - 2y$ .
The combined expression is $4 - 3$ .
The combined expression is $x^2 - y^2$ .