Factor 48 − 8 X 48 - 8x 48 − 8 X To Identify The Equivalent Expressions.Choose 2 Answers:A. 3 ( 16 − 8 X 3(16 - 8x 3 ( 16 − 8 X ] B. 2 ( 24 − 4 X 2(24 - 4x 2 ( 24 − 4 X ] C. 8 ( 6 − X 8(6 - X 8 ( 6 − X ] D. 4 ( 12 − 4 X 4(12 - 4x 4 ( 12 − 4 X ]

Introduction

Factoring is a fundamental concept in algebra that involves expressing an algebraic expression as a product of simpler expressions. In this article, we will focus on factoring the expression $48 - 8x$ to identify its equivalent expressions. We will explore the different methods of factoring and provide step-by-step solutions to help you understand the concept better.

Understanding the Expression

Before we proceed with factoring, let's understand the given expression. The expression $48 - 8x$ consists of two terms: a constant term $48$ and a variable term $-8x$. Our goal is to factor this expression into simpler terms.

Factoring the Expression

To factor the expression $48 - 8x$, we need to find the greatest common factor (GCF) of the two terms. The GCF is the largest expression that divides both terms without leaving a remainder. In this case, the GCF of $48$ and $-8x$ is $8$.

We can factor out the GCF $8$ from both terms as follows:

$$48 - 8x = 8(6 - x)$$

Analyzing the Factored Form

Now that we have factored the expression, let's analyze the factored form. The factored form is $8(6 - x)$, which consists of two terms: a constant term $8$ and a variable term $(6 - x)$. The variable term $(6 - x)$ is a linear expression that represents a line with a slope of $-1$ and a y-intercept of $6$.

Comparing with the Options

Now that we have factored the expression, let's compare it with the given options. We have four options to choose from:

A. $3(16 - 8x)$ B. $2(24 - 4x)$ C. $8(6 - x)$ D. $4(12 - 4x)$

Conclusion

Based on our analysis, we can conclude that the correct answer is:

C. $8(6 - x)$

This is because the factored form of the expression $48 - 8x$ is indeed $8(6 - x)$. The other options do not match the factored form, and therefore, are incorrect.

Tips and Tricks

Here are some tips and tricks to help you factor expressions like $48 - 8x$:

• Always look for the greatest common factor (GCF) of the two terms.
• Factor out the GCF from both terms.
• Analyze the factored form to understand the expression better.
• Compare the factored form with the given options to choose the correct answer.

Practice Problems

Here are some practice problems to help you practice factoring expressions like $48 - 8x$:

• Factor the expression $24 - 4x$.
• Factor the expression $36 - 6x$.
• Factor the expression $48 - 12x$.

Conclusion

Introduction

In our previous article, we discussed how to factor the expression $48 - 8x$ to identify its equivalent expressions. We also provided some tips and tricks to help you factor expressions like $48 - 8x$. In this article, we will answer some frequently asked questions (FAQs) related to factoring expressions.

Q: What is factoring?

A: Factoring is a fundamental concept in algebra that involves expressing an algebraic expression as a product of simpler expressions. It involves finding the greatest common factor (GCF) of the terms and factoring it out.

Q: How do I find the greatest common factor (GCF) of two terms?

A: To find the GCF of two terms, you need to look for the largest expression that divides both terms without leaving a remainder. You can use the following steps to find the GCF:

1. List the factors of each term.
2. Identify the common factors.
3. Choose the largest common factor.

Q: What are some common mistakes to avoid when factoring expressions?

A: Here are some common mistakes to avoid when factoring expressions:

• Not looking for the greatest common factor (GCF) of the terms.
• Factoring out the wrong term.
• Not analyzing the factored form to understand the expression better.
• Not comparing the factored form with the given options to choose the correct answer.

Q: How do I factor expressions with multiple terms?

A: To factor expressions with multiple terms, you need to follow these steps:

1. Look for the greatest common factor (GCF) of the terms.
2. Factor out the GCF from each term.
3. Analyze the factored form to understand the expression better.
4. Compare the factored form with the given options to choose the correct answer.

Q: What are some real-world applications of factoring expressions?

A: Factoring expressions has many real-world applications, including:

• Algebraic geometry: Factoring expressions is used to study the properties of curves and surfaces.
• Number theory: Factoring expressions is used to study the properties of integers and modular forms.
• Cryptography: Factoring expressions is used to develop secure encryption algorithms.

Q: How do I practice factoring expressions?

A: Here are some ways to practice factoring expressions:

• Practice factoring expressions with different numbers of terms.
• Practice factoring expressions with different types of terms (e.g., linear, quadratic, polynomial).
• Practice factoring expressions with different levels of difficulty.
• Use online resources, such as factoring calculators and worksheets, to practice factoring expressions.

Q: What are some common types of expressions that require factoring?

A: Here are some common types of expressions that require factoring:

• Linear expressions: Expressions with one variable and a constant term.
• Quadratic expressions: Expressions with two variables and a constant term.
• Polynomial expressions: Expressions with multiple variables and constant terms.
• Rational expressions: Expressions with a numerator and a denominator.

Conclusion

In conclusion, factoring expressions is a fundamental concept in algebra that involves expressing an algebraic expression as a product of simpler expressions. By understanding the concept of factoring and practicing it regularly, you can develop your problem-solving skills and apply them to real-world problems.