Combine Like Terms To Find The Equivalent Expression Of $5y - 3y + 12$.The New Expression Becomes:A. $8y + 12$B. $-2y + 12$C. $2y + 12$D. $14y$

Introduction

Algebra is a branch of mathematics that deals with solving equations and manipulating variables. One of the fundamental concepts in algebra is combining like terms, which involves simplifying expressions by adding or subtracting terms with the same variable. In this article, we will explore how to combine like terms to find the equivalent expression of $5y - 3y + 12$.

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

Combining Like Terms

To combine like terms, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Step-by-Step Solution

Now, let's apply the order of operations to the given expression $5y - 3y + 12$:

1. Parentheses: There are no expressions inside parentheses, so we can move on to the next step.
2. Exponents: There are no exponential expressions, so we can move on to the next step.
3. Multiplication and Division: There are no multiplication and division operations, so we can move on to the next step.
4. Addition and Subtraction: We have two terms with the same variable $y$, which are $5y$ and $-3y$. We can combine these terms by adding their coefficients (the numbers in front of the variable).

Combining the Like Terms

To combine the like terms $5y$ and $-3y$, we add their coefficients:

$5y - 3y = (5 - 3)y = 2y$

So, the expression $5y - 3y$ simplifies to $2y$.

Adding the Constant Term

Now, we need to add the constant term $12$ to the simplified expression $2y$:

$2y + 12$

The Final Answer

Therefore, the equivalent expression of $5y - 3y + 12$ is $2y + 12$.

Conclusion

Combining like terms is an essential skill in algebra that helps us simplify expressions and solve equations. By following the order of operations and combining like terms, we can simplify complex expressions and make them easier to work with. In this article, we have seen how to combine like terms to find the equivalent expression of $5y - 3y + 12$. We hope this article has been helpful in understanding the concept of combining like terms in algebra.

Answer Key

The correct answer is:

C. $2y + 12$

Additional Examples

Here are some additional examples of combining like terms:

• $3x + 2x - 4x = (3 + 2 - 4)x = x$
• $4y - 2y + 6y = (4 - 2 + 6)y = 8y$
• $2x + 5x - 3x = (2 + 5 - 3)x = 4x$

Introduction

In our previous article, we explored the concept of combining like terms in algebra and provided a step-by-step guide on how to simplify expressions by adding or subtracting terms with the same variable. In this article, we will answer some frequently asked questions about combining like terms to help you better understand this concept.

Q&A

Q: What are like terms in algebra?

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 combine like terms?

A: To combine like terms, you need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

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

A: Combining like terms is a specific technique used to simplify expressions by adding or subtracting terms with the same variable. Simplifying expressions, on the other hand, involves rewriting an expression in a simpler form by combining like terms, removing parentheses, and performing other operations.

Q: Can I combine unlike terms?

A: No, unlike terms cannot be combined. 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: How do I know if two terms are like terms?

A: To determine if two terms are like terms, you need to check if they have the same variable raised to the same power. If they do, then they are like terms and can be combined.

Q: Can I combine terms with different coefficients?

A: Yes, you can combine terms with different coefficients. For example, $2x$ and $5x$ can be combined to get $7x$.

Q: What is the final answer to the expression $5y - 3y + 12$?

A: The final answer to the expression $5y - 3y + 12$ is $2y + 12$.

Q: Can you provide more examples of combining like terms?

A: Here are some additional examples of combining like terms:

• $3x + 2x - 4x = (3 + 2 - 4)x = x$
• $4y - 2y + 6y = (4 - 2 + 6)y = 8y$
• $2x + 5x - 3x = (2 + 5 - 3)x = 4x$

Q: How do I apply the order of operations to combine like terms?

A: To apply the order of operations to combine like terms, you need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Conclusion

Combining like terms is an essential skill in algebra that helps us simplify expressions and solve equations. By following the order of operations and combining like terms, we can simplify complex expressions and make them easier to work with. We hope this Q&A guide has been helpful in understanding the concept of combining like terms in algebra.

Answer Key

The correct answers to the questions are:

• Q1: Like terms are terms that have the same variable raised to the same power.
• Q2: To combine like terms, you need to follow the order of operations (PEMDAS).
• Q3: Combining like terms is a specific technique used to simplify expressions by adding or subtracting terms with the same variable.
• Q4: No, unlike terms cannot be combined.
• Q5: To determine if two terms are like terms, you need to check if they have the same variable raised to the same power.
• Q6: Yes, you can combine terms with different coefficients.
• Q7: The final answer to the expression $5y - 3y + 12$ is $2y + 12$.
• Q8: Yes, here are some additional examples of combining like terms: $3x + 2x - 4x = (3 + 2 - 4)x = x$, $4y - 2y + 6y = (4 - 2 + 6)y = 8y$, $2x + 5x - 3x = (2 + 5 - 3)x = 4x$.
• Q9: To apply the order of operations to combine like terms, you need to follow the order of operations (PEMDAS).