Simplify The Expression: 8 X − 2 ( X + 3 8x - 2(x + 3 8 X − 2 ( X + 3 ]Choose The Correct Simplified Form From The Options Below:A. 6 X + 6 6x + 6 6 X + 6 B. 6 X + 3 6x + 3 6 X + 3 C. 6 X − 6 6x - 6 6 X − 6 D. 6 X − 5 6x - 5 6 X − 5

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the expression $8x - 2(x + 3)$ using the distributive property and combining like terms.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside. In the given expression, we have $8x - 2(x + 3)$, and we need to apply the distributive property to simplify it.

Applying the Distributive Property

To simplify the expression, we will apply the distributive property by multiplying each term inside the parentheses with the term outside. This means we will multiply $8x$ with $-2$ and $3$ with $-2$.

8x - 2(x + 3) = 8x - 2x - 6

Combining Like Terms

Now that we have expanded the expression, we can combine like terms to simplify it further. Like terms are terms that have the same variable raised to the same power. In this case, we have $8x$ and $-2x$, which are like terms.

8x - 2x = 6x

Simplifying the Expression

Now that we have combined like terms, we can simplify the expression by subtracting $6$ from the result.

6x - 6

Conclusion

In conclusion, the simplified form of the expression $8x - 2(x + 3)$ is $6x - 6$. This is the correct answer among the options provided.

Answer Options

Here are the answer options:

• A. $6x + 6$
• B. $6x + 3$
• C. $6x - 6$
• D. $6x - 5$

Correct Answer

The correct answer is C. $6x - 6$.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions like this:

• Always apply the distributive property to expand expressions.
• Combine like terms to simplify expressions.
• Check your work by plugging in values or using a calculator.

Practice Problems

Here are some practice problems to help you practice simplifying expressions:

• Simplify the expression $3x - 2(x - 4)$.
• Simplify the expression $2x + 5(x + 2)$.
• Simplify the expression $4x - 3(x - 1)$.

Conclusion

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Introduction

In our previous article, we discussed how to simplify the expression $8x - 2(x + 3)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside. For example, in the expression $8x - 2(x + 3)$, we can apply the distributive property to get $8x - 2x - 6$.

Q: How do I know which terms to combine?

A: To combine like terms, you need to identify the terms that have the same variable raised to the same power. In the expression $8x - 2x$, we can combine the terms because they both have the variable $x$ raised to the power of 1.

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. For example, in the expression $8x - 2y$, $8x$ and $2y$ are unlike terms because they have different variables.

Q: Can I simplify expressions with fractions?

A: Yes, you can simplify expressions with fractions by applying the distributive property and combining like terms. For example, in the expression $\frac{1}{2}x - \frac{1}{3}(x + 2)$, you can apply the distributive property to get $\frac{1}{2}x - \frac{1}{3}x - \frac{2}{3}$.

Q: How do I simplify expressions with exponents?

A: To simplify expressions with exponents, you need to apply the rules of exponents. For example, in the expression $2^3 \cdot 2^2$, you can simplify it by adding the exponents to get $2^5$.

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

A: Yes, you can simplify expressions with variables in the denominator by applying the rules of fractions. For example, in the expression $\frac{x}{2} - \frac{x}{3}$, you can simplify it by finding a common denominator to get $\frac{3x - 2x}{6}$.

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

A: To check your work, you can plug in values or use a calculator to evaluate the expression. For example, if you simplify the expression $8x - 2(x + 3)$ to get $6x - 6$, you can plug in a value for $x$ to check if the expression is true.

Conclusion

Simplifying expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. By answering these FAQs, we hope to provide you with a better understanding of how to simplify expressions and how to apply the distributive property and combining like terms.

Practice Problems

Here are some practice problems to help you practice simplifying expressions:

• Simplify the expression $3x - 2(x - 4)$.
• Simplify the expression $2x + 5(x + 2)$.
• Simplify the expression $4x - 3(x - 1)$.

Additional Resources

Here are some additional resources to help you learn more about simplifying expressions:

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• IXL: Simplifying Expressions

Conclusion

We hope this article has provided you with a better understanding of how to simplify expressions and how to apply the distributive property and combining like terms. Remember to practice regularly and to check your work to ensure that you are getting the correct answers.