Simplify The Expression: $\[ 17a + 25b + 13a - 7b \\]A. $\[ 30a + 18b \\] B. $\[ 48ab \\] C. $\[ 42ab + 6ab \\] D. $\[ 42a + 6b \\]

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill to master. In this article, we will focus on simplifying the given expression: $17a + 25b + 13a - 7b$. We will break down the steps involved in simplifying this expression and provide a clear understanding of the process.

Understanding the Expression

The given expression is a combination of two terms: $17a + 25b$ and $13a - 7b$. To simplify this expression, we need to combine like terms, which are terms that have the same variable raised to the same power.

Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, the like terms are $17a$ and $13a$, and $25b$ and $-7b$.

Simplifying the Expression

To simplify the expression, we need to combine the like terms. We can do this by adding or subtracting the coefficients of the like terms.

Step 1: Combine the Like Terms

The first step is to combine the like terms $17a$ and $13a$. To do this, we add the coefficients of these terms, which are $17$ and $13$. The result is $30a$.

# Combine the like terms 17a and 13a
a_coefficient = 17 + 13
print(f"The result of combining 17a and 13a is {a_coefficient}a")

Step 2: Combine the Like Terms

The next step is to combine the like terms $25b$ and $-7b$. To do this, we add the coefficients of these terms, which are $25$ and $-7$. The result is $18b$.

# Combine the like terms 25b and -7b
b_coefficient = 25 - 7
print(f"The result of combining 25b and -7b is {b_coefficient}b")

Step 3: Combine the Results

The final step is to combine the results of the previous steps. We have $30a$ and $18b$, so the simplified expression is $30a + 18b$.

Conclusion

In this article, we simplified the given expression $17a + 25b + 13a - 7b$ by combining like terms. We broke down the steps involved in simplifying this expression and provided a clear understanding of the process. The final simplified expression is $30a + 18b$.

Answer

The correct answer is:

• A. $30a + 18b$

Explanation

The correct answer is A because it is the simplified expression that results from combining the like terms in the given expression.

Comparison with Other Options

Let's compare the correct answer with the other options:

• B. $48ab$ is incorrect because it is not the simplified expression that results from combining the like terms in the given expression.
• C. $42ab + 6ab$ is incorrect because it is not the simplified expression that results from combining the like terms in the given expression.
• D. $42a + 6b$ is incorrect because it is not the simplified expression that results from combining the like terms in the given expression.

Conclusion

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Introduction

In our previous article, we discussed how to simplify algebraic expressions by combining like terms. In this article, we will provide a Q&A guide to help you understand the concept better.

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.

Q: How do I identify like terms?

A: To identify like terms, you need to look for terms that have the same variable raised to the same power. For example, in the expression $3x + 2y + 4x - 5y$, the like terms are $3x$ and $4x$, and $2y$ and $-5y$.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, in the expression $3x + 2y + 4x - 5y$, the like terms are $3x$ and $4x$, and $2y$ and $-5y$. To combine these like terms, you add the coefficients: $3 + 4 = 7$ for the $x$ terms, and $2 - 5 = -3$ for the $y$ terms. The resulting expression is $7x - 3y$.

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

A: When combining like terms, you need to follow the order of operations:

1. Identify the like terms.
2. Add or subtract the coefficients of the like terms.
3. Combine the like terms.

Q: Can I combine unlike terms?

A: No, you cannot combine unlike terms. Unlike terms are terms that have different variables or variables raised to different powers. For example, $2x$ and $3y$ are unlike terms and cannot be combined.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms is a step in simplifying an expression. Simplifying an expression involves combining like terms, removing any unnecessary parentheses, and rearranging the terms in a way that makes the expression easier to read and understand.

Q: How do I know when to combine like terms?

A: You should combine like terms whenever you have an expression that contains multiple terms with the same variable raised to the same power. Combining like terms can help simplify the expression and make it easier to work with.

Q: Can I use a calculator to combine like terms?

A: Yes, you can use a calculator to combine like terms. However, it's always a good idea to do the calculations by hand to make sure you understand the process and to avoid any potential errors.

Conclusion

In conclusion, combining like terms is an essential skill in algebra that can help simplify expressions and make them easier to work with. By following the order of operations and understanding what like terms are, you can combine like terms with confidence.

Frequently Asked Questions

• Q: What are some common mistakes to avoid when combining like terms? A: Some common mistakes to avoid when combining like terms include forgetting to add or subtract the coefficients, not identifying like terms correctly, and not following the order of operations.
• Q: How do I know if I have combined like terms correctly? A: To check if you have combined like terms correctly, you can plug the expression into a calculator or simplify it by hand to see if you get the same result.
• Q: Can I combine like terms with negative coefficients? A: Yes, you can combine like terms with negative coefficients. For example, $-3x + 2x$ can be combined to get $-x$.

Additional Resources

• Algebra textbooks: Check out algebra textbooks for more information on combining like terms and simplifying expressions.
• Online resources: Visit online resources such as Khan Academy, Mathway, or Wolfram Alpha for interactive lessons and practice problems on combining like terms.
• Practice problems: Practice combining like terms with sample problems and exercises to help you build your skills and confidence.