First, Rewrite The Expression By Combining Like Terms. 3 B + 4 + 10 + 6 B − 2 = □ B + □ 3b + 4 + 10 + 6b - 2 = \square B + \square 3 B + 4 + 10 + 6 B − 2 = □ B + □

Mar 13, 2025 by ADMIN 164 views

**Simplifying Algebraic Expressions: Combining Like Terms**

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 rewriting the expression $3b + 4 + 10 + 6b - 2$ by combining like terms.

Understanding 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. On the other hand, $2x$ and $3y$ are not like terms because they have different variables.

Rewriting the Expression

To rewrite the expression $3b + 4 + 10 + 6b - 2$ , we need to combine the like terms. The like terms in this expression are the terms with the variable $b$ . We can combine these terms by adding their coefficients.

# Define the coefficients of the like terms
coefficient_1 = 3
coefficient_2 = 6
sum_coefficients = coefficient_1 + coefficient_2

print("The sum of the coefficients is:", sum_coefficients)

The sum of the coefficients is 9. Therefore, the expression can be rewritten as $9b + 4 + 10 - 2$ .

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression further by combining the constants. The constants in this expression are 4, 10, and -2. We can combine these constants by adding them.

# Define the constants
constant_1 = 4
constant_2 = 10
constant_3 = -2

sum_constants = constant_1 + constant_2 + constant_3

print("The sum of the constants is:", sum_constants)

The sum of the constants is 12. Therefore, the expression can be rewritten as $9b + 12$ .

Conclusion

In this article, we have learned how to rewrite the expression $3b + 4 + 10 + 6b - 2$ by combining like terms. We have also learned how to simplify the expression further by combining the constants. By following these steps, we can simplify complex algebraic expressions and make them easier to work with.

Example Use Cases

Combining like terms is a fundamental concept in algebra that has many practical applications. Here are a few example use cases:

Simplifying equations: Combining like terms can help simplify equations and make them easier to solve.
Solving systems of equations: Combining like terms can help simplify systems of equations and make them easier to solve.
Graphing functions: Combining like terms can help simplify functions and make them easier to graph.

Tips and Tricks

Here are a few tips and tricks to help you combine like terms:

Identify the like terms: The first step in combining like terms is to identify the like terms in the expression.
Combine the coefficients: Once you have identified the like terms, combine their coefficients by adding them.
Simplify the expression: Finally, simplify the expression by combining the constants.

Common Mistakes

Here are a few common mistakes to avoid when combining like terms:

Not identifying the like terms: Failing to identify the like terms is a common mistake that can lead to incorrect results.
Not combining the coefficients: Failing to combine the coefficients is another common mistake that can lead to incorrect results.
Not simplifying the expression: Failing to simplify the expression is a common mistake that can lead to incorrect results.

Conclusion

Introduction

Combining like terms is a fundamental concept in algebra that can be a bit tricky to understand at first. However, with practice and patience, you can master this skill and become proficient in simplifying complex algebraic expressions. In this article, we will answer some of the most frequently asked questions about combining like terms.

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 $3x + 2y + 4x - 2y$ , the like terms are $3x$ and $4x$ because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. For example, in the expression $3x + 4x$ , the coefficients are 3 and 4. To combine these terms, you add their coefficients: $3 + 4 = 7$ . Therefore, the expression can be rewritten as $7x$ .

Q: What if I have a negative coefficient?

A: If you have a negative coefficient, you need to subtract the coefficient from the other coefficient. For example, in the expression $3x - 4x$ , the coefficients are 3 and -4. To combine these terms, you subtract the coefficients: $3 - 4 = -1$ . Therefore, the expression can be rewritten as $-x$ .

Q: Can I combine like terms with different variables?

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

Q: What if I have a fraction as a coefficient?

A: If you have a fraction as a coefficient, you need to multiply the fraction by the other coefficient. For example, in the expression $2x + \frac{3}{4}x$ , the coefficients are 2 and $\frac{3}{4}$ . To combine these terms, you multiply the fraction by the other coefficient: $2 \times \frac{3}{4} = \frac{6}{4}$ . Therefore, the expression can be rewritten as $2x + \frac{3}{2}x$ .

Q: Can I combine like terms with exponents?

A: Yes, you can combine like terms with exponents. For example, in the expression $2x^2 + 3x^2$ , the coefficients are 2 and 3. To combine these terms, you add their coefficients: $2 + 3 = 5$ . Therefore, the expression can be rewritten as $5x^2$ .

Q: What if I have a variable with a coefficient of 1?

A: If you have a variable with a coefficient of 1, you can omit the coefficient. For example, in the expression $1x + 2x$ , you can omit the coefficient 1 and rewrite the expression as $x + 2x$ .

Conclusion

In conclusion, combining like terms is a fundamental concept in algebra that can be a bit tricky to understand at first. However, with practice and patience, you can master this skill and become proficient in simplifying complex algebraic expressions. Remember to identify the like terms, combine their coefficients, and simplify the expression to get the correct result.