Simplify:${ \left(4u^2 - 2u + 7\right) + \left(-5u^2 + 3u + 1\right) }$

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 focus on simplifying the given expression by combining like terms.

The Given Expression

The given expression is:

$$\left(4u^2 - 2u + 7\right) + \left(-5u^2 + 3u + 1\right)$$

Step 1: Identify Like Terms

To simplify the expression, we need to identify like terms. Like terms are terms that have the same variable and exponent. In this expression, we can identify the following like terms:

• Terms with the variable $u^2$: $4u^2$ and $-5u^2$
• Terms with the variable $u$: $-2u$ and $3u$
• Constant terms: $7$ and $1$

Step 2: Combine Like Terms

Now that we have identified the like terms, we can combine them. To combine like terms, we add or subtract the coefficients of the terms.

• Combine the terms with the variable $u^2$: $4u^2 - 5u^2 = -u^2$
• Combine the terms with the variable $u$: $-2u + 3u = u$
• Combine the constant terms: $7 + 1 = 8$

Simplified Expression

After combining the like terms, the simplified expression is:

$$-u^2 + u + 8$$

Conclusion

In this article, we simplified the given expression by combining like terms. We identified the like terms, combined them, and arrived at the simplified expression. This process helps simplify complex expressions and makes them easier to work with.

Real-World Applications

Combining like terms is a fundamental concept in algebra that has real-world applications in various fields, such as physics, engineering, and economics. It helps simplify complex expressions and makes them easier to work with.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions by combining like terms:

• Identify like terms carefully: Make sure to identify like terms correctly to avoid errors.
• Combine like terms systematically: Combine like terms in a systematic way to avoid confusion.
• Check your work: Check your work to ensure that you have combined the like terms correctly.

Common Mistakes

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

• Failing to identify like terms: Failing to identify like terms can lead to incorrect simplification.
• Combining unlike terms: Combining unlike terms can lead to incorrect simplification.
• Not checking work: Not checking work can lead to errors.

Practice Problems

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

• Simplify the expression: $2x^2 + 3x + 1 + 4x^2 - 2x - 3$
• Simplify the expression: $5y^2 - 2y + 1 + 3y^2 + 4y - 2$
• Simplify the expression: $6z^2 + 2z - 1 + 2z^2 - 3z + 4$

Conclusion

Q&A: Simplifying Expressions by Combining Like Terms

Frequently Asked Questions

In this article, we will answer some frequently asked questions about simplifying expressions by combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x^2$ and $4x^2$ are like terms because they both have the variable $x$ and the exponent $2$.

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. You can do this by comparing the coefficients of the terms and the variables.

Q: What is the difference between combining like terms and adding or subtracting terms?

A: Combining like terms involves adding or subtracting terms that have the same variable and exponent. Adding or subtracting terms involves adding or subtracting terms that have the same variable and exponent, but also taking into account the signs of the terms.

Q: Can I combine unlike terms?

A: No, you cannot combine unlike terms. Unlike terms are terms that have different variables or exponents. Combining unlike terms can lead to incorrect simplification.

Q: How do I simplify an expression with multiple like terms?

A: To simplify an expression with multiple like terms, you need to identify the like terms, combine them, and then simplify the resulting expression.

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

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

• Failing to identify like terms
• Combining unlike terms
• Not checking work
• Not following the order of operations

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

A: To check your work when simplifying expressions by combining like terms, you need to:

• Identify the like terms
• Combine the like terms
• Simplify the resulting expression
• Check the expression to ensure that it is correct

Q: What are some real-world applications of simplifying expressions by combining like terms?

A: Simplifying expressions by combining like terms has real-world applications in various fields, including:

• Physics: Simplifying expressions by combining like terms is used to solve problems involving motion, energy, and momentum.
• Engineering: Simplifying expressions by combining like terms is used to design and optimize systems, such as bridges and buildings.
• Economics: Simplifying expressions by combining like terms is used to analyze and model economic systems.

Q: How can I practice simplifying expressions by combining like terms?

A: You can practice simplifying expressions by combining like terms by:

• Working on practice problems
• Using online resources, such as calculators and worksheets
• Asking a teacher or tutor for help
• Joining a study group or online community

Conclusion

In conclusion, simplifying expressions by combining like terms is a fundamental concept in algebra that has real-world applications in various fields. By identifying like terms, combining them systematically, and checking work, you can simplify complex expressions and make them easier to work with.