Simplify The Expression: − C + ( − 6 C ) + ( − 3 C ) + ( − 8 C ) + ( − 6 C ) − 9 C -c + (-6c) + (-3c) + (-8c) + (-6c) - 9c − C + ( − 6 C ) + ( − 3 C ) + ( − 8 C ) + ( − 6 C ) − 9 C

Mar 10, 2025 by ADMIN 181 views

**Simplify the Expression: A Step-by-Step Guide**

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves combining like terms, which are terms that have the same variable raised to the same power. In this article, we will simplify the expression $-c + (-6c) + (-3c) + (-8c) + (-6c) - 9c$ using a step-by-step approach.

Understanding the Expression

The given expression is $-c + (-6c) + (-3c) + (-8c) + (-6c) - 9c$ . At first glance, it may seem complex, but let's break it down and understand what's happening. We have several terms, each with a variable $c$ and a coefficient (a number that multiplies the variable). The coefficients are $-1$ , $-6$ , $-3$ , $-8$ , $-6$ , and $-9$ .

Step 1: Combine Like Terms

To simplify the expression, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have several terms with the variable $c$ . We can combine these terms by adding or subtracting their coefficients.

-c + (-6c) + (-3c) + (-8c) + (-6c) - 9c

Let's combine the terms with the variable $c$ :

(-1c) + (-6c) + (-3c) + (-8c) + (-6c) + (-9c)

Now, let's add the coefficients of the terms with the variable $c$ :

-1c - 6c - 3c - 8c - 6c - 9c

Step 2: Simplify the Coefficients

Now that we have combined the like terms, let's simplify the coefficients. We can do this by adding or subtracting the coefficients.

-1c - 6c - 3c - 8c - 6c - 9c

Let's add the coefficients:

-1 - 6 - 3 - 8 - 6 - 9

Now, let's simplify the coefficients:

-33

Step 3: Write the Simplified Expression

Now that we have simplified the coefficients, let's write the simplified expression. We can do this by replacing the original expression with the simplified expression.

-c + (-6c) + (-3c) + (-8c) + (-6c) - 9c = -33c

Conclusion

In this article, we simplified the expression $-c + (-6c) + (-3c) + (-8c) + (-6c) - 9c$ using a step-by-step approach. We combined like terms, simplified the coefficients, and wrote the simplified expression. The simplified expression is $-33c$ . This is a crucial skill in mathematics, and it helps us solve problems efficiently.

Tips and Tricks

When simplifying expressions, always combine like terms first.
When combining like terms, add or subtract the coefficients.
When simplifying coefficients, add or subtract the coefficients.
When writing the simplified expression, replace the original expression with the simplified expression.

Common Mistakes

Not combining like terms first.
Not adding or subtracting coefficients correctly.
Not simplifying coefficients correctly.
Not writing the simplified expression correctly.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics, and it has many real-world applications. For example, in physics, we use simplifying expressions to solve problems involving motion and energy. In engineering, we use simplifying expressions to design and optimize systems. In economics, we use simplifying expressions to model and analyze economic systems.

Final Thoughts

Introduction

In our previous article, we simplified the expression $-c + (-6c) + (-3c) + (-8c) + (-6c) - 9c$ using a step-by-step approach. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms. For example, if we have the terms $2x$ and $-3x$ , we can combine them by adding the coefficients: $2x - 3x = -x$ .

Q: What is the order of operations when simplifying expressions?

A: The order of operations when simplifying expressions is:

Combine like terms
Simplify coefficients
Write the simplified expression

Q: Can I simplify expressions with variables in the denominator?

A: Yes, you can simplify expressions with variables in the denominator. However, you need to follow the rules of exponents and fractions.

Q: How do I simplify expressions with negative coefficients?

A: To simplify expressions with negative coefficients, follow the same steps as simplifying expressions with positive coefficients. The negative sign will be carried over to the simplified expression.

Q: Can I simplify expressions with multiple variables?

A: Yes, you can simplify expressions with multiple variables. However, you need to follow the rules of exponents and combine like terms carefully.

Q: What is the difference between simplifying expressions and factoring expressions?

A: Simplifying expressions involves combining like terms and simplifying coefficients, while factoring expressions involves expressing an expression as a product of simpler expressions.

Q: How do I know when to simplify an expression?

A: You should simplify an expression when:

The expression is complex and difficult to work with
The expression has multiple like terms
The expression has negative coefficients
The expression has variables in the denominator

Q: Can I simplify expressions with absolute values?

A: Yes, you can simplify expressions with absolute values. However, you need to follow the rules of absolute values and simplify the expression carefully.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, plug in a value for the variable and evaluate the expression. If the result is correct, then your simplification is correct.

Conclusion

Simplifying expressions is a crucial skill in mathematics, and it has many real-world applications. By following the steps outlined in this article and answering the frequently asked questions, you can become proficient in simplifying expressions and solve problems efficiently.

Tips and Tricks

Always combine like terms first
Simplify coefficients carefully
Write the simplified expression clearly
Check your work by plugging in a value for the variable
Practice, practice, practice!

Common Mistakes

Not combining like terms first
Not simplifying coefficients carefully
Not writing the simplified expression clearly
Not checking work by plugging in a value for the variable
Not practicing enough!

Real-World Applications

Final Thoughts

Simplifying expressions is a crucial skill in mathematics, and it helps us solve problems efficiently. By following the steps outlined in this article and answering the frequently asked questions, you can become proficient in simplifying expressions and solve problems efficiently. Remember to always combine like terms first, simplify coefficients carefully, write the simplified expression clearly, and check your work by plugging in a value for the variable. With practice and patience, you can become proficient in simplifying expressions and solve problems efficiently.