Combine Like Terms In The Expression: { -5a - 8b + 3a + 11b$}$

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 and exponent. In this article, we will explore how to combine like terms in the given expression: ${-5a - 8b + 3a + 11b}$. We will break down the process step by step and provide examples to illustrate the concept.

What are Like Terms?

Like terms are terms that have the same variable and exponent. For example, in the expression ${2x + 3x}$, the terms ${2x}$ and ${3x}$ are like terms because they both have the variable ${x}$ and the same exponent (which is 1). Similarly, in the expression ${4y^2 + 2y^2}$, the terms ${4y^2}$ and ${2y^2}$ are like terms because they both have the variable ${y}$ and the same exponent (which is 2).

Step 1: Identify the Like Terms

To combine like terms, we need to identify the terms that have the same variable and exponent. In the given expression ${-5a - 8b + 3a + 11b}$, we can see that the terms ${-5a}$ and ${3a}$ are like terms because they both have the variable ${a}$ and the same exponent (which is 1). Similarly, the terms ${-8b}$ and ${11b}$ are like terms because they both have the variable ${b}$ and the same exponent (which is 1).

Step 2: Combine the Like Terms

Once we have identified the like terms, we can combine them by adding or subtracting their coefficients. In the given expression, we have two sets of like terms: ${-5a + 3a}$ and ${-8b + 11b}$. We can combine these terms by adding their coefficients:

${-5a + 3a = -2a}$ ${-8b + 11b = 3b}$

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by combining the resulting terms:

${-2a + 3b}$

Conclusion

Combining like terms is an essential concept in algebra that helps simplify complex expressions. By identifying the like terms and combining their coefficients, we can simplify the expression and make it easier to work with. In this article, we have seen how to combine like terms in the given expression ${-5a - 8b + 3a + 11b}$. We have broken down the process step by step and provided examples to illustrate the concept.

Examples

Here are some examples of combining like terms:

• ${2x + 3x = 5x}$
• ${4y^2 + 2y^2 = 6y^2}$
• ${-3a + 2a = -a}$
• ${-5b + 11b = 6b}$

Tips and Tricks

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

• Make sure to identify the like terms correctly before combining them.
• Use the correct operation (addition or subtraction) when combining the like terms.
• Simplify the expression by combining the resulting terms.
• Check your work by plugging in values for the variables.

Common Mistakes

Here are some common mistakes to avoid when combining like terms:

• Failing to identify the like terms correctly.
• Using the wrong operation (addition or subtraction) when combining the like terms.
• Not simplifying the expression by combining the resulting terms.
• Not checking your work by plugging in values for the variables.

Real-World Applications

Combining like terms has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, combining like terms can help simplify complex equations that describe the motion of objects. In engineering, combining like terms can help simplify complex equations that describe the behavior of electrical circuits. In economics, combining like terms can help simplify complex equations that describe the behavior of economic systems.

Conclusion

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Introduction

Combining like terms is a fundamental concept in algebra that helps simplify complex expressions. In our previous article, we explored how to combine like terms in the expression ${-5a - 8b + 3a + 11b}$. In this article, we will answer some frequently asked questions about combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, in the expression ${2x + 3x}$, the terms ${2x}$ and ${3x}$ are like terms because they both have the variable ${x}$ and the same exponent (which is 1).

Q: How do I identify like terms?

A: To identify like terms, you need to look for terms that have the same variable and exponent. For example, in the expression ${-5a - 8b + 3a + 11b}$, the terms ${-5a}$ and ${3a}$ are like terms because they both have the variable ${a}$ and the same exponent (which is 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 ${-5a - 8b + 3a + 11b}$, we can combine the like terms ${-5a + 3a}$ and ${-8b + 11b}$ by adding their coefficients:

${-5a + 3a = -2a}$ ${-8b + 11b = 3b}$

Q: What if I have a negative coefficient?

A: If you have a negative coefficient, you need to change the sign of the term when combining like terms. For example, in the expression ${-5a + 3a}$, the negative coefficient ${-5a}$ becomes ${5a}$ when combining like terms.

Q: Can I combine like terms with different exponents?

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

Q: How do I simplify the expression after combining like terms?

A: After combining like terms, you need to simplify the expression by combining the resulting terms. For example, in the expression ${-2a + 3b}$, we can simplify the expression by combining the terms:

${-2a + 3b}$

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

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

• Failing to identify the like terms correctly.
• Using the wrong operation (addition or subtraction) when combining the like terms.
• Not simplifying the expression by combining the resulting terms.
• Not checking your work by plugging in values for the variables.

Q: How do I check my work when combining like terms?

A: To check your work when combining like terms, you need to plug in values for the variables and simplify the expression. For example, in the expression ${-2a + 3b}$, we can plug in the value ${a = 2}$ and ${b = 3}$ to get:

${-2(2) + 3(3) = -4 + 9 = 5}$

Conclusion

Combining like terms is an essential concept in algebra that helps simplify complex expressions. By identifying the like terms and combining their coefficients, we can simplify the expression and make it easier to work with. In this article, we have answered some frequently asked questions about combining like terms and provided examples to illustrate the concept.

Additional Resources

For more information on combining like terms, you can check out the following resources:

• Khan Academy: Combining Like Terms
• Mathway: Combining Like Terms
• Algebra.com: Combining Like Terms

Practice Problems

Here are some practice problems to help you practice combining like terms:

• ${2x + 3x = }$
• ${4y^2 + 2y^2 = }$
• ${-3a + 2a = }$
• ${-5b + 11b = }$

Answer Key

Here are the answers to the practice problems:

• ${2x + 3x = 5x}$
• ${4y^2 + 2y^2 = 6y^2}$
• ${-3a + 2a = -a}$
• ${-5b + 11b = 6b}$